Binary Manipulation



  1. Teacher shows how to produce binary representations for the decimal numbers 6 and 3.

  2. Teacher shows how to convert binary to decimal and shows verifies the result 110 produces 6 and 3 produces 11.

Binary Addition

  • Teacher adds 6 (110) and 3 (11) and verifies the result

Binary Subtraction

  • Teacher subtracts 6 (110) and 3 (11) and verifies the result as 3 (11)

Sign And Magnitude

  • Teacher shows how the fixed point system is used with  the MSB used to represent the sign, 0 for +ve, 1 for –ve

Twos complement

  • Show the +ve representation for 6 and 3

  • Show –ve representation of 6 and 3 (Using flip_+1 and copy+1 methods)
    • Copy method :
      • Going from right to left, copy all digits up to and including the first 1.
      • Filp the remaining bits.

  • Verify that 6-3 is equivalent to 6 + (-3 ) for an 8 bit two’s complement system.

In twos complement the MSB is taken to be -ve

Exercise – The Largest and Smallest magnitude twos complement numbers using 4 bits

Using a 4 bit twos complement system, what’s the

  1. Largest +ve number ,
  2. Lowest  -ve number

That can be represented?

© 2023  Vedesh Kungebeharry. All rights reserved. 

Decimal to binary

Task: Create an algorithm which accepts a decimal integer and outputs it’s binary equivalent.

This algorithm was designed and implemented in Flowgorithm:

See the video below for an explanation of how the algorithm works:

Decimal to binary algorithm explained

The code in C is shown below:

Copy and paste from here:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>//library needed for string operations

int main()
    //declare and identify integers
    int number, remainder;

    //declare, identify and initialize all strings
    char  result[20]="";
    char  remainderString[20]="";

    //initialize all other variables

    //get input
    printf("Enter a number in decimal\n");
    scanf("%d", &number);

    while (number!=0)

            /* #Implementation_Result

                Here we implement the following:

                    result=remainder + result

            //first convert the remainder to a string,
            //and store the converted data in "remainderString"

            //add "remainderString" to "result" in that order.
            //the result of the concatenation is stored in "remainderString"

            //now copy our data so far back to "result"
            /*End #Implementation_Result*/



    printf("The binary Result is %s \n",result);
    return 0;

© 2019  Vedesh Kungebeharry. All rights reserved.