Every calculation a computer does comes down to adding bits. Inside the processor, a circuit called an adder adds two binary numbers column by column, just as you add on paper, but it only has room for a fixed number of bits. In this lesson you will add binary numbers by hand, see the logic gates that do it in hardware, find out what happens when the answer is too big for its register (overflow), and watch the same thing happen in C. It follows on from Power Protection and Types of Computers, and it builds on word size from Memory Types and Features.

What you will learn

• The four rules for adding one column of bits, plus the rule for a column with a carry in.
• How to add two 4-bit or 8-bit numbers, showing every carry, and how to check the answer in decimal.
• How a half adder and a full adder are built from logic gates, and how full adders join to make a ripple-carry adder.
• What overflow is, how to spot it, and the range of unsigned numbers that n bits can hold.
• How C stores the result of adding two unsigned values, and why it can print an answer that looks wrong.

Part 1: A quick reminder about place values

In binary, each column is worth twice the column to its right: 1, 2, 4, 8, 16, 32, 64, 128 and so on. To read a binary number, add the place values of the columns that hold a 1. For example, 0110 1101 = 64 + 32 + 8 + 4 + 1 = 109. We write long binary numbers in groups of four bits so they are easier to read. (If you need more practice converting, see Decimal to binary and Binary Manipulation.)

Part 2: Adding binary numbers by hand

The rules for one column

There are only two digits, so a column fills up quickly. As soon as a column adds up to 2 or more, you write down the units digit and carry 1 to the next column on the left, exactly like carrying a ten in decimal.

The last row matters most. Every column except the rightmost one may receive a carry from the right, so it can have three bits to add. The total is never more than 3, so the carry out of a column is never more than 1.

Worked example 1: a 4-bit sum

Add 0101 (5) and 0011 (3). Write the carries above the columns as you go, starting from the right.

Carry    1 1 1
A        0 1 0 1     (5)
B      + 0 0 1 1     (3)
         -------
Sum      1 0 0 0     (8)

1. Column 1 (value 1): 1 + 1 = 2 = binary 10. Write 0, carry 1.
2. Column 2 (value 2): 0 + 1 + carry 1 = 2. Write 0, carry 1.
3. Column 3 (value 4): 1 + 0 + carry 1 = 2. Write 0, carry 1.
4. Column 4 (value 8): 0 + 0 + carry 1 = 1. Write 1, carry 0.
5. Check: 1000 = 8, and 5 + 3 = 8. ✔

Notice how one carry can travel (“ripple”) through several columns. Keep that picture in mind: it is exactly how the hardware adder in Part 3 works.

Worked example 2: an 8-bit sum

Add 0110 1101 (109) and 0011 1011 (59).

Carry    1111 111
A        0110 1101     (109)
B      + 0011 1011     (59)
         ---------
Sum      1010 1000     (168)

Every column from the right produces a carry until the leftmost column, which has 0 + 0 + carry 1 = 1 and so carries nothing out. Check: 1010 1000 = 128 + 32 + 8 = 168, and 109 + 59 = 168. ✔ Step through this sum yourself in Try it 1, then try your own numbers.

Always check in decimal. Convert both numbers and the answer to decimal. If the decimal sum does not match, look for a column where you forgot a carry. That is the most common mistake.

Part 3: Adders in hardware

The processor’s arithmetic logic unit (ALU) adds with logic gates. If the gates are new to you, read Logic Gates – Formal Introduction first. Look back at the column rules and compare them with the gate truth tables:

• The bit you write is 1 when exactly one of the two bits is 1. That is the XOR gate.
• The bit you carry is 1 only when both bits are 1. That is the AND gate.

Half adder

A half adder adds two bits, A and B. It has two outputs: Sum = A XOR B, and Carry = A AND B. It is called "half" because it has no input for a carry coming from the right, so it can only be used for the rightmost column.

Full adder

A full adder adds three bits: A, B and the carry in (C_in) from the column on the right. It can be built from two half adders and an OR gate:

• Sum = A XOR B XOR C_in (the sum is 1 when an odd number of the inputs are 1).
• Carry out = (A AND B) OR ((A XOR B) AND C_in) (the carry is 1 when at least two of the inputs are 1).

Read each row as an ordinary sum and the table makes sense: the two outputs, C_out then Sum, are just the total of the three inputs written in binary. For example, the last row is 1 + 1 + 1 = 3 = binary 11.

Ripple-carry adder

To add two 8-bit numbers, chain 8 full adders side by side, one per column. The carry out of each adder is wired to the carry in of the adder on its left. (The rightmost adder’s carry in is set to 0, or it can be a half adder.) This is a ripple-carry adder, because a carry may have to ripple through every stage before the answer is ready. That is exactly what you saw in Worked example 2. The two numbers usually come from registers, and the answer is stored in a register, which is a row of flip-flops like the one in The SR Latch.

Wider adders are slower, because the last column has to wait for the carry to arrive. Real processors use faster designs (such as carry-lookahead adders), but CAPE expects you to know the half adder, the full adder and how they are joined.

Part 4: Fixed width and overflow

A register, and an adder, has a fixed number of bits. That number is usually the processor’s word size (see Memory Types and Features). With n bits, the unsigned whole numbers you can store go from 0 to 2ⁿ − 1.

Adding two n-bit numbers can give an answer that needs n + 1 bits. If the register has only n bits, the extra bit (the carry out of the leftmost column) is lost. This is called overflow.

Worked example 3: overflow in 8 bits

Add 1100 1000 (200) and 0110 0100 (100) in an 8-bit register.

Carry  1 1
A        1100 1000     (200)
B      + 0110 0100     (100)
         ---------
Full   1 0010 1100     (300)
Kept     0010 1100     (44)

The true answer, 300, needs 9 bits. The register keeps only the lowest 8 bits, 0010 1100, which is 44. The 256 that the lost carry was worth has gone: 300 − 256 = 44.

Rule for unsigned numbers: the addition overflowed if, and only if, there is a carry out of the leftmost column. A 1 in the leftmost sum bit is not overflow. For example, 0100 + 0100 = 1000 (4 + 4 = 8) fits in 4 bits.

A look ahead. When the same bits stand for signed numbers (two’s complement, the next lesson), the rule changes: the carry out is simply thrown away, and overflow happens when two numbers with the same sign give an answer with the other sign. Try it 3 shows both readings so that you can compare them.

Part 5: Binary addition in C

C variables have fixed widths too. On most computers an unsigned char has 8 bits, an unsigned short has 16 bits and an unsigned int has 32 bits. When the total of an unsigned addition is too big, C does what the hardware does: it keeps the lowest bits and drops the carry. (If printf and format specifiers are new to you, see Variables, format specifiers and printf.)

#include <stdio.h>

int main(void)
{
    unsigned char a = 200;  /* 1100 1000 */
    unsigned char b = 100;  /* 0110 0100 */

    /* sum keeps only 8 bits */
    unsigned char sum = a + b;

    /* full has room for the carry */
    unsigned int full = a + b;

    printf("Full total: %u\n", full);
    printf("Kept in 8 bits: %d\n", sum);

    if (full > 255)
        printf("Overflow: carry lost\n");

    return 0;
}

Output:

Full total: 300
Kept in 8 bits: 44
Overflow: carry lost

a + b is worked out in a wider type (C first turns small types into int), so full really is 300. When the result is stored in the 8-bit sum, only the lowest 8 bits fit, so it becomes 44. That is Worked example 3 again. For unsigned types, C guarantees this wrap-around: the result is the remainder after dividing by 2ⁿ.

Warning about signed types. If a signed int overflows, the C standard says the behaviour is undefined: the program may print a strange number, or the compiler may assume it never happens. Use unsigned types when you want wrap-around, and check ranges before you add.

A ripple-carry adder in C

This program adds two 8-bit numbers the way the hardware does: one column at a time, from right to left, passing the carry along. Each pass of the loop is one full adder. The bits are kept in arrays (see Arrays in C), with bit 0, the rightmost bit, stored first.

#include <stdio.h>

int main(void)
{
    /* Bit 0 (the rightmost bit) is   */
    /* stored first, so the bits look */
    /* backwards.                     */

    /* 0110 1101 = 109 */
    int a[8] = {1,0,1,1,0,1,1,0};
    /* 0011 1011 = 59 */
    int b[8] = {1,1,0,1,1,1,0,0};
    int sum[8];
    int carry = 0;
    int total, i;

    /* one full adder per column, */
    /* from right to left         */
    for (i = 0; i < 8; i++)
    {
        /* total is 0, 1, 2 or 3 */
        total = a[i] + b[i] + carry;
        sum[i] = total % 2;  /* write */
        carry = total / 2;   /* carry */
    }

    printf("Sum:       ");
    for (i = 7; i >= 0; i--)
        printf("%d", sum[i]);
    printf("\nCarry out: %d\n", carry);

    return 0;
}

Output:

Sum:       10101000
Carry out: 0

That is 168, the answer to Worked example 2. Notice that total % 2 gives the sum bit and total / 2 gives the carry, the same as reading the full adder truth table as an ordinary sum. Change the arrays to hold 200 and 100 and run it again: the carry out becomes 1, which means overflow.

Summary

Practice questions

Homework

1. Make up three pairs of 8-bit numbers: one whose sum fits easily, one that only just fits (a total of exactly 255) and one that overflows. Add each pair by hand, showing the carries, then check them with Try it 1 and Try it 3.
2. Draw a 4-bit ripple-carry adder as four boxes labelled "Full adder". Label every input and output, and show where the carries go. Then trace 0111 + 0110 through your diagram, writing the value on every wire.
3. Copy the ripple-carry program into Code::Blocks. Change it so that it also converts the sum back to decimal and prints it. (Hint: add 2 to the power of i for every sum bit that is 1.)

Exam tips

• 2009 Unit 1 Paper 02, Question 1(d)(ii). This part asks you to add two 4-bit binary numbers whose total does not fit in 4 bits. It tests careful column-by-column carrying and whether you notice that the answer has grown to five bits. Show your carry row, give the full answer, and say in words that it cannot be stored in four bits. The other parts of 1(d) move on to reading binary in decimal, the largest and smallest values in four bits, and two’s complement, so revise them together. Try it yourself first, then compare with the solution on this site: 2009 U1 Q1.
• Specimen Unit 1 Paper 01 (2021), Item 5. A multiple-choice item on what the term word size means. It tests whether you know that the word size is the number of bits the processor handles at once, which is also the width of its registers and adder and so sets the overflow limit in this lesson. Open the specimen paper and try it before you check the key.
• Coming next: Specimen Unit 1 Paper 01 (2021), Items 1 and 2, and 2024 Unit 1 Paper 02, Question 2(c). These give an 8-bit pattern or a negative number and ask about its signed magnitude or two’s complement form, or about the range of signed values in 8 bits. They belong to the next lesson, but they rely on the fixed-width addition you practised here. See the solution 2024 U1 Q2 once you have tried it.
• Half and full adders. Adders are named in the syllabus (Unit 1, Module 1, Specific Objective 2), but I have not found a question on them in the past papers, specimen papers or solutions on this site so far. Learn the two truth tables and the Boolean expressions anyway, and be ready to draw both circuits.
• More worked answers are on the CS Solutions page.

General advice (from the lesson content, not from a particular paper): always show the carry row; write binary in groups of four; check every answer in decimal; and when a question gives a number of bits, keep exactly that many bits and say clearly whether the answer overflowed.

Previous: Power Protection and Types of Computers. Related: Memory Types and Features (word size) and The SR Latch (how a register stores bits). Next: signed numbers, two’s complement and signed overflow (coming soon in this course). For extra practice now, see Binary Manipulation and the Data Representation Homework Exercise.

Syllabus link: CAPE Computer Science (CXC A19/U2/21), Unit 1, Module 1: Computer Architecture. Specific Objective 2: describe the basic building blocks of a computer (truth tables; logic gates; adders). Specific Objective 3: interpret the interaction among the basic building blocks of a computer (logic gates, registers). Specific Objective 4: explain how data is represented in a computer system (bits; bytes; number bases). U1 M1 SO2, SO3, SO4.

Video search terms

Search YouTube for: "binary addition with carries", "half adder and full adder explained", "ripple carry adder", "unsigned integer overflow".

Attributions to media used in this post:

Half adder diagram: Inductiveload, public domain, via Wikimedia Commons (File:Half Adder.svg).

Full adder diagram: Inductiveload, public domain, via Wikimedia Commons (File:Full-adder logic diagram.svg).

Updates

11 Nov 2026

- Draft created.

© 2026 Vedesh Kungebeharry. All rights reserved.

Memory (also called main memory or primary memory) is the part of a computer that holds the instructions and data the CPU is working with. The CPU reads from it and, for some types, writes to it, using an address for each location. In this lesson we look at the memory types (RAM, ROM, EPROM and EEPROM) and the features used to compare them (speed, size, word size and volatility).

If you did CSEC, Inside the Computer: Input, Processing, Memory, Storage and Output (IPOS) is a short refresher on RAM and ROM. Here we go further.

Where the bits are kept

Every memory chip is a grid of tiny cells, and each cell stores one bit (a 0 or a 1). You have already met a circuit that can do this: the flip-flop. A flip-flop has two stable states, so once it is set or reset it keeps that bit for as long as it has power. See Flip Flops, The SR Flip-Flop – Practical Introduction and The SR Latch.

• Static RAM (SRAM) stores each bit in a flip-flop. It is fast and does not need refreshing, but each cell needs several transistors, so it costs more and holds less. Cache memory is made of SRAM.
• Dynamic RAM (DRAM) stores each bit as a charge on a tiny capacitor. The charge leaks away, so the cells must be refreshed thousands of times a second. DRAM is cheaper and holds more, so it is used for the main RAM in PCs and phones.
• The registers inside the CPU are also groups of flip-flops, one per bit. An 8-bit register is 8 flip-flops side by side.

Either way, when the power goes, the flip-flops and capacitors lose their state. That is why RAM is volatile.

Memory types

RAM (Random Access Memory)

RAM is read/write memory. It holds the operating system, the programs that are open and the data they are using. Random access means any location can be reached directly by its address, in the same time, wherever it is. RAM is fast, but it is volatile: its contents are lost when the power is switched off.

ROM (Read Only Memory)

ROM is written once, when the chip is made, and after that it can only be read. It is non-volatile, so its contents are still there when the power comes back on. ROM is used for programs that must never change, such as the control program in a washing machine or microwave, and, in older computers, the start-up (boot) program.

EPROM (Erasable Programmable ROM)

An EPROM can be programmed, erased and programmed again. To erase it, the chip is taken out of the circuit and ultraviolet (UV) light is shone through a small quartz window on top of it, usually for several minutes. This erases the whole chip. A device called a programmer then writes the new contents. EPROM is non-volatile.

Image: EPROM AM27C256DC by Anonimski, CC BY-SA 3.0, via Wikimedia Commons.

EEPROM (Electrically Erasable Programmable ROM)

An EEPROM is erased and rewritten electrically, so it can be changed while it stays in the circuit, one byte at a time. Writing is much slower than writing to RAM, and each cell can only be rewritten a limited number of times, so it is used for data that changes now and then, like settings. EEPROM is non-volatile.

Flash memory is a type of EEPROM that erases in blocks instead of single bytes, which makes it faster to rewrite. It is used for the BIOS/UEFI firmware on motherboards, USB flash drives, memory cards, SSDs and phone storage.

Memory features

Volatility

Volatile memory needs power to keep its contents; non-volatile memory keeps them with the power off. RAM is volatile. ROM, EPROM, EEPROM and flash are non-volatile. This is why you must save your work to storage, and why the first instructions a computer runs at power on have to come from ROM or flash: RAM is empty at that moment.

Speed

Speed is how quickly data can be read from or written to memory, often given as the access time. Electronic memory has no moving parts, so its access time is measured in nanoseconds. A hard disk has to move its read/write head and wait for the disk to spin, so its access time is measured in milliseconds. In general, the closer the memory is to the CPU, the faster and smaller (and more expensive per byte) it is: registers, then cache, then RAM, then secondary storage.

Size (capacity)

Size is how much the memory can hold, measured in bytes (KB, MB, GB). Each location has its own address. With n address lines there are 2ⁿ different addresses, so:

capacity = number of locations × word size

For example, 10 address lines give 2¹⁰ = 1,024 locations. If each location holds an 8-bit word, the capacity is 1,024 bytes, which is 1 KB.

Word size

The word size is how many bits the CPU works on in a single operation. It is usually the size of the CPU’s registers and the amount of data moved to or from memory in one go. Most computers and phones today are 64-bit; small microcontrollers may be 8-bit or 16-bit. A larger word size lets the CPU work on bigger numbers in one step and move more data per memory access.

Variables live in RAM: a C example

When your C program runs, it is loaded into RAM, and every variable you declare is given some bytes of RAM at an address. The program below declares an int, then prints its value, how many bytes it uses (sizeof) and its address (%p). The & in &x means "the address of x". (Recap: Variables, Format Specifiers and printf (%d), and for addresses, C Pointers.)

#include <stdio.h>

int main()
{
    int x = 5;

    printf("Value: %d\n", x);
    printf("Bytes: %d\n", (int) sizeof(x));
    printf("Address: %p\n", (void *) &x);

    return 0;
}

Run it in Code::Blocks. The first line will show Value: 5. The number of bytes depends on your compiler (on most desktop compilers an int is 4 bytes, which is 32 bits). The address is printed in hexadecimal and will be different on your computer, and it may change each time you run the program, because the operating system decides where in RAM the program goes. When the program ends, or the power goes, that RAM is given back and the value of x is gone: volatility in action.

You can also watch variables change while a program runs in the debugger: see Adding 2 numbers, declaring integer variables, watching variables.

Practice questions

Homework

1. Make a table that compares RAM, ROM, EPROM and EEPROM under these headings: read/write, volatility, how it is erased, one use.
2. Find the RAM size and the word size (32-bit or 64-bit) of a computer or phone at home. Write down where you found the information.

Exam tips

• Specimen Unit 1 Paper 01 (2021), Items 4, 5, 7 and 8. Four multiple-choice items on this lesson, all with syllabus reference 1.1 (Module 1). Item 4 is about what cache memory is for, Item 5 is about the meaning of word size, Item 7 is about which memory family flash memory belongs to, and Item 8 is about which memory or storage device is slowest to access. They test whether you know the definitions exactly and can rank devices by speed (registers, cache, RAM, then storage). Read every option before you choose, because a wrong option is often a true statement about a different part of the computer. Open the specimen paper and try all four items before you check the answer key.
• Specimen Unit 1 Paper 02 (2021), Question 2(a). This part asks you to tell two pairs of memory types apart, ROM and RAM, then EPROM and EEPROM, with 2 marks for each pair. It tests whether you can make a clear contrast. Make one point about each item, on the same feature (for example whether it can be written to, or how it is erased), so that each half of your contrast can earn a mark. A point about only one of the two items cannot earn both marks. Try it on paper, then compare with practice questions 1 and 2 above.
• 2024 Unit 1 Paper 02, Question 1(b). Two parts that compare devices on named features: a hard disk with RAM (access method and access speed), and RAM with a flash drive (volatility and portability), 3 marks each. It tests whether you can apply the memory features to real devices. Cover every named feature for both devices, use the feature words in your answer, and give a reason (for example, moving parts make a hard disk slower). Try it first, then read the solution on this site: 2024 U1 Q1. See also Serial, Sequential, Direct (Random) Access.
• More worked answers are on the CS Solutions page.

Background: Flip Flops, The SR Flip-Flop – Practical Introduction and The SR Latch. Next: registers and the CPU (coming soon in this course). For a first look at how the CPU uses its registers to fetch instructions from memory, see 2009 U1 Q2 Part C and part (a) of 2024 U1 Q1.

Syllabus link: CAPE Computer Science (CXC A19/U2/21), Unit 1, Module 1: Computer Architecture. Specific Objective 1: state the purpose of the main components of a computer system (memory types: ROM, RAM, EPROM, EEPROM; memory features: speed, size, word size, volatility). U1 M1 SO1.

Attributions to media used in this post:

EPROM chip photo: Anonimski, CC BY-SA 3.0, via Wikimedia Commons (File:EPROM AM27C256DC.jpg).

Updates

7 Nov 2026: Added the shared course badge summary and lesson mastery quiz, with feedback, retries and browser-saved progress.

27 Oct 2026

- Draft created.

28 Oct 2026

- Exam references reworded and quiz questions rewritten.

© 2026 Vedesh Kungebeharry. All rights reserved.

A storage device (also called secondary storage or backing storage) keeps programs and data permanently, even when the power is off. Your files, your apps and the operating system itself all live on storage until they are needed, and then they are copied into RAM so the CPU can work on them. We compare storage devices using four features: capacity, access speed, access method and portability.

This lesson follows on from Memory Types and Features. If you did CSEC, Inside the Computer: Input, Processing, Memory, Storage and Output (IPOS) is a short refresher.

Storage and memory are not the same

The four features

Capacity

Capacity is how much data the device can hold, measured in bytes: MB, GB and TB. Remember 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB and 1 TB = 1024 GB. (Drive makers often use 1000 instead of 1024, which is why a new “1 TB” drive shows a little less space on a computer.)

Access speed

Access speed is how quickly data can be found and read or written. Two measures are used:

• Access time: how long it takes to find the data. On a hard disk this is the seek time (moving the head to the right track) plus the rotational delay (waiting for the right sector to spin under the head).
• Data transfer rate: how much data can be moved per second once it has been found, e.g. 150 MB/s.

Devices with moving parts (tape, hard disk, optical disc) are slower to access than solid state devices, which find data electronically.

Access method

The access method is the way the device gets to a particular piece of data:

• Sequential (serial) access: the data is read in order from the start, so to reach a record, every record before it must be passed. Magnetic tape works this way.
• Direct (random) access: the device can go straight to the data using its address. Disks (magnetic and optical) and solid state devices work this way. A hard disk is sometimes called semi-random, because the head goes straight to the track but then waits for the sector to come round.

More on this in Serial, Sequential, Direct (Random) Access and File Organisation and Access Methods.

Portability

Portability is how easily the device (and its data) can be carried and used on another computer. Small size, low weight, no separate power supply, a common connector such as USB, and the ability to survive knocks all make a device more portable. A USB flash drive is very portable; an internal hard disk is not meant to be moved.

Types of storage devices

Magnetic storage: hard disk and tape

A hard disk drive (HDD) stores data magnetically on spinning metal or glass platters. Each platter surface is divided into circular tracks, and each track into sectors. A read/write head on an actuator arm moves across the platter to the right track. Hard disks give a large capacity at a low cost per GB and allow direct access, but because of the moving parts they are slower than SSDs, use more power and can be damaged if dropped while running.

Image: Hard drive.svg by Surachit, CC BY-SA 3.0, via Wikimedia Commons.

Magnetic tape stores data on a long plastic tape coated with magnetic material, wound inside a cartridge. Access is sequential, so finding one file can take a long time. But a tape cartridge holds a huge amount of data (18 TB or more) very cheaply and lasts for years, so tape is used by banks, businesses and data centres for backups and archives, where the data is written and read in order anyway.

Optical storage: CD, DVD and Blu-ray

Optical discs store data as tiny pits and flat areas (lands) along one long spiral track. A laser shines on the track and the drive detects how the light is reflected. Blu-ray uses a blue-violet laser with a shorter wavelength than the red laser of a DVD, so the pits can be smaller and packed closer together, giving more capacity.

• CD: about 700 MB. DVD: 4.7 GB (8.5 GB dual layer). Blu-ray: 25 GB per layer (50 GB dual layer).
• -ROM discs are pressed at the factory and are read only; -R discs can be written once; -RW discs can be erased and rewritten.
• Optical discs allow direct access but are slow, and they are cheap, light and very portable. They are used for distributing films, music and software, and for small backups, but they are much less common now than flash drives and the cloud.

Solid state storage: SSD, flash drive and memory card

Solid state devices store data in flash memory chips, a type of EEPROM (see Memory Types and Features). There are no moving parts, so they find data very quickly, use little power, are silent and survive knocks better than hard disks. They cost more per GB than hard disks, and each cell can only be rewritten a limited number of times.

• Solid state drive (SSD): replaces the hard disk inside most laptops and many desktops, so the computer starts and opens programs much faster.
• USB flash drive: pocket-sized, plugs into a USB port, ideal for carrying files between computers.
• Memory card (SD, microSD): tiny, used in cameras, phones, drones and game consoles.

Cloud storage

Cloud storage keeps your files on a provider’s servers (for example Google Drive or OneDrive), which you reach over the Internet. The real storage devices are hard disks and SSDs in the provider’s data centres. Capacity depends on your plan, there is nothing to carry, and your files are backed up off site. But you need an Internet connection, the speed depends on that connection, and you are trusting the provider with your data. See Cloud Storage vs Local Storage.

Capacity and copying time

To check whether data fits, compare its size with the capacity, using the same unit. To estimate the copying time, divide the size by the transfer rate:

time (seconds) = size (MB) ÷ transfer rate (MB/s)

For example, a 4 GB video is 4 × 1024 = 4096 MB. At 100 MB/s it takes 4096 ÷ 100 ≈ 41 seconds. Watch the units: Internet speeds are given in megabits per second (Mbps), and there are 8 bits in a byte, so a 10 Mbps upload is only 10 ÷ 8 = 1.25 MB/s.

Files live on storage: a C example

In Memory Types and Features we saw that a variable lives in RAM and is lost when the program ends. To keep a value, a program must write it to a file on a storage device. The first program below saves the value of score to a file with fopen and fwrite. The second program, run later (even after a restart), reads it back with fread.

#include <stdio.h>

int main()
{
    int score = 95;
    FILE *f = fopen("score.dat", "wb");

    if (f == NULL)
    {
        printf("Could not open file\n");
        return 1;
    }

    fwrite(&score, sizeof(score), 1, f);
    fclose(f);
    printf("Saved %d\n", score);

    return 0;
}

#include <stdio.h>

int main()
{
    int score = 0;
    FILE *f = fopen("score.dat", "rb");

    if (f == NULL)
    {
        printf("Could not open file\n");
        return 1;
    }

    fread(&score, sizeof(score), 1, f);
    fclose(f);
    printf("Read %d\n", score);

    return 0;
}

"wb" means write in binary mode and "rb" means read in binary mode. fwrite copies the bytes of score from RAM to the file, and fread copies them from the file back into RAM. Notice that the second program starts with score = 0, so any other value it prints must have come from storage. If you would rather store data as readable text, see Tutorial: Storing and loading data in a plain textfile.

Practice questions

Homework

1. Copy the comparison table from Try it 2 into your notebook. Add a column "One suitable use" and fill it in for each device.
2. Find the storage on a computer or phone at home: the type (HDD, SSD or flash), the capacity and how much is free. Write down where you found the information.

Exam tips

• Specimen Unit 1 Paper 01 (2021), Item 8. A multiple-choice item on comparing how quickly different memory and storage devices give access to data (syllabus reference 1.1, Module 1). It tests whether you can rank electronic memory against storage devices, including older removable media you may not have used yourself. Put the options in order of speed in your head (registers, cache, RAM, then storage, with moving parts slowest) before you choose. Open the specimen paper and try it before you check the answer key.
• 2024 Unit 1 Paper 02, Question 1(b). Two parts that compare a storage device with RAM: a hard disk against RAM on access method and access speed, and RAM against a flash drive on volatility and portability, 3 marks each. It tests whether you can use the storage features from this lesson to explain a difference. For each named feature, say something about both devices and give a reason, for example the head has to move to the track and wait for the sector, so hard disk access is measured in milliseconds. Try it first, then compare with the solution on this site: 2024 U1 Q1.
• 2017 and 2018 Unit 2 Paper 02, Question 5. Storage comes back in Unit 2 with virtual memory, where pages of processes that do not fit in RAM are kept on the hard disk. Try the questions, then see the solutions on this site: 2017 U2 Q5 and 2018 U2 Q5.
• More worked answers are on the CS Solutions page.

General advice for storage questions (from the lesson content, not from a particular paper): when asked to choose a device, name it and justify it using the four features, capacity, access speed, access method and portability, linked to the scenario.

Previous: Memory Types and Features. Next: the processor (CPU) and how it fetches instructions and data from memory (coming soon in this course; for now see 2009 U1 Q2 Part C). After that, data representation: how the bits on these devices stand for numbers and characters (Decimal to binary, Binary Manipulation).

Syllabus link: CAPE Computer Science (CXC A19/U2/21), Unit 1, Module 1: Computer Architecture. Specific Objective 1: state the purpose of the main components of a computer system (storage devices: capacity, access speed, access method, portability). U1 M1 SO1.

Attributions to media used in this post:

Hard disk diagram: Surachit, CC BY-SA 3.0, via Wikimedia Commons (File:Hard drive.svg).

Updates

7 Nov 2026: Added the shared course badge summary and lesson mastery quiz, with feedback, retries and browser-saved progress.

27 Oct 2026

- Draft created.

28 Oct 2026

- Exam references reworded and quiz questions rewritten.

© 2026 Vedesh Kungebeharry. All rights reserved.

An input device sends data and instructions into a computer, for example a keyboard, mouse, microphone, scanner or sensor. An output device takes the results of processing out of the computer in a form people (or other machines) can use, for example a monitor, printer or speakers. Some devices, such as a touch screen, do both. When we compare input and output devices we look at port connectivity (how they connect), speed and the quality of output.

This is the third lesson on the parts of a computer, after Memory Types and Features and Storage Devices. If you did CSEC, Choosing the Right Input and Output Devices is a short refresher.

Port connectivity

A port is a socket on the computer where a device is connected. The port decides what the cable can carry (data, power, video, sound or a network) and how fast. Many devices now connect wirelessly instead, using Bluetooth or Wi-Fi. When a device is connected, the operating system uses a small program called a device driver to talk to it.

Things to think about when choosing a connection: does the computer have that port; is the port fast enough for the device (a webcam or external SSD needs more speed than a mouse); does the cable also need to carry power or sound; and would wireless be more convenient (no cable), or is wired better (faster, more reliable, no batteries to charge)?

Speed

Speed means different things for different devices:

• Input speed: how quickly data can be entered. A keyboard is limited by how fast a person types. A barcode reader, or the MICR reader that reads the magnetic ink numbers on bank cheques, enters data much faster and with fewer errors, because no one types it.
• Printer speed is measured in pages per minute (ppm). Laser printers are usually faster than inkjet printers for large amounts of text.
• Monitor speed is the refresh rate in hertz (Hz): how many times a second the picture is redrawn. 60 Hz is normal; gaming monitors use 144 Hz or more for smoother movement.
• Connection speed: the port or wireless link must be fast enough for the data (see the table above).

Quality of output

The quality of output is how good the result looks or sounds.

• Screens: the resolution is the number of pixels across and down, for example 1920 × 1080 (Full HD) or 3840 × 2160 (4K). More pixels give a sharper picture. The colour depth is the number of bits used for each pixel’s colour: 24 bits gives 2²⁴, about 16.7 million colours.
• Printers: quality is measured in dots per inch (dpi). A laser printer gives sharp text (typically 600 dpi or more) and is cheap per page for large jobs. An inkjet printer gives good colour photos and is cheap to buy, but the ink is expensive per page. A dot-matrix (impact) printer is noisy and gives low quality, but it can print on multi-part forms, where a copy is made by pressing through the sheets.
• Sound: better speakers and headphones give clearer sound with less distortion.

Higher quality costs something: more pixels and more colours mean bigger files, more memory and more data to send through the port.

Specialised devices

The syllabus names four specialised devices. Each one solves a particular problem.

Braille keyboard

A braille keyboard lets a blind or visually impaired person type by touch. Some are ordinary keyboards with raised braille dots on the keys. Others have six main keys, one for each dot of a braille cell, as on a Perkins Brailler: you press the keys for the dots together to make one letter. Braille users often also use a refreshable braille display (an output device whose pins rise and fall to show text as braille) and a screen reader, software that reads the screen aloud.

Image: Perkins brailler keyboard layout by Emflazie, CC0 (public domain), via Wikimedia Commons.

Sensors

A sensor is an input device that measures a physical quantity, such as temperature, light, moisture, pressure, humidity or movement. Most sensors give an analogue signal, so an analogue-to-digital converter (ADC) turns it into a binary number the computer can process. Sensors are used in monitoring and control systems, for example greenhouses, security alarms, traffic lights and car parking sensors. They take readings automatically and continuously, day and night, and are more accurate than a person.

In a control system, the computer compares each reading with a set value called the threshold. If the reading crosses it, the computer sends a signal to an actuator (a motor, fan, pump, lamp or alarm) to switch on or off.

Touch screen

A touch screen is both an output device (the display) and an input device (it detects where it is touched). A resistive touch screen detects pressure, so it works with a stylus or gloves. A capacitive touch screen detects the small electrical charge of a finger, is more sensitive and supports multi-touch, such as pinching to zoom. Touch screens are used on phones, tablets, ATMs, airport kiosks and shop tills. They are easy to learn and need no keyboard or mouse, but they get fingerprints, are slow for typing a lot of text, and small buttons are hard to hit. That is why the buttons on this page are at least 48 pixels tall.

Concept keyboard

A concept keyboard is a flat board divided into areas. Each area stands for a whole item or idea, not a single letter, and is shown by a picture or word on an overlay. The areas can be programmed for each use. Concept keyboards are used on fast-food tills (one press for "large fries"), and by young children and people with learning difficulties. Data entry is fast with few errors, and the sealed surface is easy to wipe clean and resists spills. The drawback is that only a fixed set of choices can be entered.

Summary

Input and output in C

In C, scanf reads input (normally from the keyboard) and printf sends output (normally to the screen). Your program does not need to know which keyboard or monitor is attached: the operating system and its device drivers deal with the actual devices.

#include <stdio.h>

int main()
{
    int age;

    printf("Enter your age: ");
    scanf("%d", &age);
    printf("Next year: %d\n", age + 1);

    return 0;
}

Whatever whole number the user types is stored in the variable age in RAM, and the program prints one more than it. More on this in Variables, format specifiers and printf and Adding 2 numbers: outputting the result with printf().

Practice questions

Homework

1. Look at the ports on a computer or laptop at home or at school. List each port, say what it is (use the table above), and name one device you could connect to it.
2. On a Windows computer, open Device Manager and list the input and output devices installed (keyboards, mice, monitors, audio). The CAPE syllabus suggests this activity.
3. Choose one specialised device from this lesson. Write a short paragraph on who uses it, what problem it solves, and one advantage and one disadvantage.

Exam tips

• Use the syllabus headings. For this objective the syllabus compares input and output devices by port connectivity, speed and quality of output, and names four specialised devices: the braille keyboard, sensors, the touch screen and the concept keyboard. When you compare devices in an answer, organise it under those headings.
• 2024 Unit 1 Paper 02, Question 2(b). Sensors turn up inside a logic question here: several sensors in a security system have to share one line, and you are asked how a multiplexer makes that possible. It tests whether you can link input devices to the building blocks from Module 1. Explain which inputs the sensors connect to, what the select lines do, and how each sensor gets the line in turn. Try it, then compare with the solution on this site: 2024 U1 Q2. See also Multiplexers.
• 2024 Unit 1 Paper 02, Question 1(b)(ii). This part compares RAM with a flash drive on volatility and portability. It tests whether you can explain portability in terms of the device itself, and the port it uses is part of that answer. The solution on this site points out that a flash drive plugs into a USB port. Try the part first, then compare.
• Specimen Unit 1 Paper 02 (2021), Question 2(b)(ii). This part is about the kinds of instruction a CPU has in its instruction set. One kind moves data, including to and from input and output devices, which is where this lesson meets the processor. For each kind you name, give a short description and an example. Try it when you study the CPU, then check the mark scheme.
• Specimen Unit 2 Paper 01 (2021), Item 45. A multiple-choice item on what happens to a running process while it waits for input from a device, and when that input arrives. It belongs to Unit 2 (operating systems: process states, device drivers, polling, buffering and spooling), so it is only a preview here. When you get there, draw the process state diagram before you choose an answer. Open the specimen paper and try it then.
• More worked answers are on the CS Solutions page.

General advice (from the lesson content, not from a particular paper): when asked to choose a device for a scenario, name the device, then justify it with the features in the question, such as who the user is, the port or connection, the speed needed and the quality of output.

Previous: Storage Devices (and before that, Memory Types and Features). Next: the processor (CPU), and how it moves data between memory and the input and output devices (coming soon in this course; for now see 2009 U1 Q2 Part C). Sensor readings become binary numbers, so data representation follows: see Decimal to binary. For how users interact with a computer, see User Interfaces: Command Line, Menus, Graphical and Touch.

Syllabus link: CAPE Computer Science (CXC A19/U2/21), Unit 1, Module 1: Computer Architecture. Specific Objective 1: state the purpose of the main components of a computer system (input/output devices: port connectivity, speed, quality of output; specialised devices: braille keyboard, sensors, touch screen, concept keyboard). U1 M1 SO1.

Attributions to media used in this post:

Braille keyboard diagram: Emflazie, CC0 1.0 (public domain), via Wikimedia Commons (File:Perkins brailler keyboard layout.png).

Updates

7 Nov 2026: Added the shared course badge summary and lesson mastery quiz, with feedback, retries and browser-saved progress.

28 Oct 2026

- Draft created.

- Exam references reworded and quiz questions rewritten.

© 2026 Vedesh Kungebeharry. All rights reserved.

Computers need a steady supply of electricity, and they come in very different sizes, from a phone in your pocket to a supercomputer that fills a hall. This lesson covers both: how to protect a computer from power problems, and the main types of computer. It is the last part of Unit 1, Module 1, Specific Objective 1, after Memory Types and Features, Storage Devices and Input and Output Devices.

What you will learn

• The common power problems: spikes, surges, sags (brownouts), over-voltage and blackouts.
• What a surge protector, a voltage regulator and an uninterruptible power supply (UPS) do, and when to use each.
• How to estimate how long a UPS can run a computer.
• The main types of computer: supercomputer, server, microcomputer (desktop) and mobile devices.
• How to choose a suitable type of computer for a task.

Part 1: Device power protection

Why power matters

In Trinidad and Tobago, and many other Caribbean islands, the mains supply is about 115 volts (V). A computer’s power supply turns this into the small, steady voltages the parts inside need. If the mains voltage jumps, drops or stops, the computer can restart, lose the data in RAM (RAM is volatile, as you saw in Memory Types and Features), damage files being written, or even be destroyed.

Power problems

Surge protector

A surge protector (surge suppressor) looks like a power strip, but inside it has parts (usually metal oxide varistors, MOVs) that send extra voltage to the earth wire when a spike or surge arrives. This protects the equipment plugged into it.

• It is rated in joules: the higher the joule rating, the more energy it can absorb before it wears out.
• It does not help with sags or blackouts.
• After a big strike it may need replacing. Many have a light that shows whether protection is still working.
• A plain power strip without surge protection gives no protection at all.

Voltage regulator

A voltage regulator (automatic voltage regulator, AVR) keeps the output voltage at a steady level. When the mains sags it boosts the voltage, and when the mains runs too high it lowers it. Use one where the supply often runs too low or too high for long periods.

• It fixes sags, brownouts and over-voltage.
• It does not help in a blackout: with no input power, there is nothing to regulate.

Uninterruptible power supply (UPS)

A UPS has a battery and an inverter (which turns the battery’s direct current back into alternating current). When the mains fails, the UPS switches to battery at once, so the computer keeps running. The aim is usually not to work for hours, but to give enough time to save work and shut down properly, or to keep a server running until a generator starts.

• Standby (offline) UPS: the cheapest. Equipment runs from the mains until it fails, then the UPS switches to battery in a few milliseconds.
• Line-interactive UPS: also has a voltage regulator, so it fixes sags and over-voltage without using the battery.
• Online (double-conversion) UPS: the equipment always runs from the inverter, so there is no switch-over gap at all. It is used for servers and medical equipment, and costs the most.
• Most UPS units include surge protection too.
• Many can tell the computer, through a USB cable, to shut down by itself when the battery is low.

Ratings. A UPS is rated in volt-amperes (VA) and in watts (W). For example, a 650 VA UPS might supply at most 390 W. Always compare the total power your devices use, in watts, with the watt rating. The battery stores energy, measured in watt-hours (Wh). A rough runtime is:

runtime in minutes ≈ battery Wh × 0.8 ÷ load in W × 60

The 0.8 allows for energy lost in the inverter and battery. For a PC and monitor using 175 W on an 86 Wh battery: 86 × 0.8 ÷ 175 × 60 ≈ 24 minutes.

Which device for which problem?

The same sum in C. If you are new to float and printf, see Variables, format specifiers and printf.

#include <stdio.h>

int main(void)
{
    float battery_wh = 86;   /* energy stored in the UPS battery */
    float load_w = 175;      /* PC 150 W + monitor 25 W */
    float minutes;

    minutes = battery_wh * 0.8 / load_w * 60;   /* about 80% is usable */
    printf("Runtime: about %.0f minutes\n", minutes);

    return 0;
}

Output: Runtime: about 24 minutes. Change load_w to 390 and run it again: the runtime falls to about 11 minutes.

Good care of your computer also includes keeping vents clear and backing up: see Taking Care of Your Computer and Backing Up and Restoring Your Work. A UPS protects against losing a few minutes of work; only a backup protects against losing everything.

Part 2: Types of computers

Computers are grouped by size, processing power, cost and how many people use them at once. The CAPE syllabus names four types. (You may also meet older names such as mainframe, a large computer used by banks and governments to process huge numbers of transactions for many users, and minicomputer, a mid-sized machine that servers have largely replaced. For a CSEC-level refresher, see Types of Computer Systems.)

Supercomputer

The fastest and most expensive type. A supercomputer links thousands of processors so that they work on parts of one huge problem at the same time (parallel processing). Its speed is measured in FLOPS (floating-point operations per second); the fastest machines in 2026 manage more than 10¹⁸ FLOPS (exascale). It needs a large room, a lot of electricity and powerful cooling.

• Uses: weather and climate models, medicine and materials research, simulating car crashes or earthquakes, space science.
• Users: research teams who submit jobs to it, often over the Internet.

Server

A server is a computer that provides a service to other computers (clients) over a network: web pages, email, shared files, databases or printing. Servers are built to run all day, every day, and often have two power supplies, spare disks (RAID) and a UPS. Many are mounted in racks in a cooled server room or data centre. You will meet servers again in networks: see Types of Computer Networks.

Microcomputer (desktop)

A microcomputer is a computer built around a single microprocessor, for one user at a time. The desktop PC is the usual example: it sits on a desk, has a separate monitor, keyboard and mouse, is cheap for the power it gives, and is easy to repair and upgrade. Laptops are microcomputers too, but because they are portable they are often grouped with mobile devices.

Mobile devices

Mobile devices are small, light and battery powered, so they can be used on the move: laptops, tablets, smartphones and wearables such as smartwatches. They usually have a touch screen, wireless connections (Wi-Fi, Bluetooth, mobile data), GPS and cameras. The trade-offs are battery life, smaller screens, less upgradability, and being easy to lose or steal.

Choosing a type of computer

Ask: How much processing does the task need? How many users at once? Must it be carried? What is the budget? Then justify your choice with those facts. There is more practice in Choosing a Suitable Computer System for a Purpose.

Summary

Practice questions

Homework

1. Find the power protection used at home or school (power strips, surge protectors, voltage regulators, UPS units). Read the label of one and write down its rating (joules, VA or W).
2. List the devices you would plug into a UPS at home, look up or estimate their watts, and use the estimator above to choose a UPS.
3. For each of the four types of computer, name one real organisation in the Caribbean or elsewhere that would use it, and say why.

Exam tips

• Specimen Unit 1 Paper 01 (2021), Item 14. A multiple-choice item that describes an organisation with a very demanding scientific task and asks which type of computer suits it best. It tests whether you can link the size of a processing job to the right type of computer. Some options are older categories that are not in the syllabus list, so know briefly what a mainframe and a minicomputer are. Look for clues about the amount of calculation and the number of users. Open the specimen paper, try it, then check the key.
• Specimen Unit 2 Paper 01 (2021), Item 42. A multiple-choice item on a network diagram, where you identify labelled parts such as a server. It belongs to Unit 2 (networks), so it is only a preview here, but it shows why you must know what a server does. Try it when you study networks.
• Power protection. I have not found a question on surge protectors, voltage regulators or UPS units in the specimen papers or in the solutions on this site so far, but they are on the syllabus list, so learn them.
• More worked answers are on the CS Solutions page.

General advice (from the lesson content, not from a particular paper): when asked to recommend a device or a type of computer, name it, then justify it with facts from the scenario. For power protection, say which power problem it deals with (spike, surge, sag, over-voltage or blackout). For a UPS, say that it gives time to save work and shut down properly. For a computer type, mention processing power, number of users, portability and cost.

Previous: Input and Output Devices (and before that, Storage Devices and Memory Types and Features). Next: the processor (CPU), the part that does the processing in every one of these computers (coming soon in this course; for now see 2009 U1 Q2 Part C).

Syllabus link: CAPE Computer Science (CXC A19/U2/21), Unit 1, Module 1: Computer Architecture. Specific Objective 1: state the purpose of the main components of a computer system (device power protection: surge protectors, voltage regulators, Uninterruptible Power Supplies (UPS); types of computers: supercomputer, server, microcomputer (desktop), mobile devices). U1 M1 SO1.

Video search terms

Search YouTube for: "how a UPS works", "surge protector explained", "automatic voltage regulator explained", "what is a supercomputer", "what is a server".

Attributions to media used in this post:

Frontier supercomputer photo: OLCF at ORNL, CC BY 2.0, via Wikimedia Commons (File:Frontier Supercomputer (2).jpg).

Updates

7 Nov 2026: Added the shared course badge summary and lesson mastery quiz, with feedback, retries and browser-saved progress.

4 Nov 2026

- Draft created.

© 2026 Vedesh Kungebeharry. All rights reserved.

Adding two binary numbers uses the same columns as decimal addition, but each column only has the digits 0 and 1. When a column totals 2 or more, you write 0 or 1 in that place and carry 1 to the next place on the left. In this lesson you will switch bits, watch the carries move, and add the same numbers in a short C program.

Syllabus link: CAPE Computer Science Unit 1, Module 1, specific objective 4 (how data is represented, including number bases).

The place values 1, 2, 4 and 8 are the columns you add. The older notes on decimal to binary show one way to convert. You met integers in Variables, format specifiers, printf %d. Continue with Binary Representation and Manipulation for signed magnitude and two’s complement. The SR Latch lesson shows how a circuit can remember one bit.

What you will learn

• Add unsigned binary numbers from right to left, showing every carry.
• Explain why a column total of 2 or 3 produces a carry.
• Distinguish the full answer from the result kept in a fixed number of bits.
• Connect binary addition to the + operator in C and the computer’s ALU.

The addition rules for one column

Each column has three inputs: the bit from the first number, the bit from the second number, and a carry in from the place on the right. Their total is 0, 1, 2 or 3. The sum bit for this place is the remainder when that total is divided by 2. The carry out is 1 when the total is 2 or 3, and 0 otherwise. That carry out becomes the carry in for the place on the left.

Start at the rightmost place. Its carry in is always 0. Write the sum bit, pass the carry out left, and repeat. If the final carry out is 1, the sum needs one extra bit on the left.

Add two 4-bit numbers

Tap a place in A or in B to include it or leave it out. The sum bits and the carries update at once. Places from the left are 8, 4, 2 and 1. Try the stacked sum below before you read the worked example.

   1011
+  0110
  -----
      ?

Worked example: follow the carries

1011 is 8 + 2 + 1 = 11. 0110 is 4 + 2 = 6. Add column by column from the right. The carry in to the units place is 0.

   1011
+  0110
  -----
  10001

Units place: 1 + 0 + 0 = 1. Write 1, carry out 0.

Twos place: 1 + 1 + 0 = 2. Write 0, carry out 1.

Fours place: 0 + 1 + 1 = 2. Write 0, carry out 1.

Eights place: 1 + 0 + 1 = 2. Write 0, carry out 1.

The final carry out is 1, so the full pattern is 10001. That is 16 + 1 = 17. 11 + 6 = 17. Set the top row A to 1011 and the bottom row B to 0110 on Try it 1 and confirm the sum.

Fixed-width check: four unsigned bits can store 0 to 15. The full answer here is 17 and needs five bits. If only the lowest four bits are kept, the stored pattern is 0001 and the final carry is lost. This is unsigned overflow; signed overflow uses a different test.

One column at a time

The rules fit in one column. Tap the three inputs. The sum bit and the carry out update. This is the step the 4-bit adder repeats from right to left.

The same addition in C

This program adds the same two numbers in decimal. The computer still does the addition in binary inside the ALU. Type it in Code::Blocks and run it. The result matches the decimal total from Try it 1.

#include <stdio.h>

int main(void) {
    int a = 11; /* binary 1011 */
    int b = 6;  /* binary 0110 */
    int sum = a + b;
    printf("The sum is %d\n", sum);
    return 0;
}

Check yourself

Answer from the columns and the carries, not from memory of a paper. Your first try is the one that counts.

   1010
+  0101
  -----
      ?

   1111
+  0001
  -----
      ?

Exam tips

Write each operand on its own line, align the place values and start at the right. Show the carries and state whether your answer includes an extra carry bit. Check the full result in decimal. For practice with exam solutions, use the CS Solutions index and open the paper named in each solution. The questions here are original practice.

Practice questions

   1101
+  0011
  -----
      ?

   1101
+  0011
  -----
  10000

   0111
+  1001
  -----
  10000

Homework

Work these out on paper before using Try it 1. Keep the numbers on separate lines and show each carry.

1. Find the full sum, then state the four stored bits and the carry out.

   1101
+  1011
  -----
      ?

2. Repeat for the next pair. Explain why this answer fits into four bits.

   0101
+  0010
  -----
      ?

   1101
+  1011
  -----
  11000

   0101
+  0010
  -----
   0111

   0101
+  0011
  -----
      ?

   1111
+  0001
  -----
      ?

   1010
+  1001
  -----
      ?

   0111
+  0001
  -----
      ?

int a = 6;
int b = 5;
printf("%d", a + b);

   1100
+  0110
  -----
      ?

Next, connect the patterns to signed numbers in Binary Representation and Manipulation, or revisit Memory Types and Features to see where bits are held.

Attributions to media used in this post:

Phlsph7, CC0 1.0 Universal Public Domain Dedication, via Wikimedia Commons.

Updates

7 Nov 2026: Added the shared course badge summary and lesson mastery quiz, with feedback, retries and browser-saved progress.

7 Nov 2026: Added a 10-question Binary Addition mastery quiz with feedback, retries and a browser-saved badge at 8/10.
6 Nov 2026: First version. Image linked directly from Wikimedia Commons.
6 Nov 2026: Matched the earlier CAPE CS lesson styling; stacked binary sums in aligned columns, added learning outcomes, fixed-width overflow guidance, homework and links to related lessons.

© 2026 Vedesh Kungebeharry. All rights reserved.