# Binary Manipulation

### Conversions

Class:

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.

• 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?