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.

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?

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