بسم الله الرحمن الرحيم

   

 

 

 

     
 

Ripple-Carry Adders:

Addition is the most frequent operation which can be used also for multiplication and division. Therefore, fast two-operand adder is very essential.

Parallel Adder with 3 FAs:

 

The above adder is called a Ripple-Carry Adder which has the following characteristics:

¨       In a parallel arithmetic unit:

*        All 2n input bits are available at the same time

*        Carries propagate from the FA in position 0 (with inputs  x0 and y0) to position i before that position produces correct sum and carry-out bits

*        Carries ripple should through all n FAs before we can claim that the sum outputs are correct and may be used in further calculations

¨       ci may change later on resulting in a change in the final sum, si

¨       Ripple effect can be observed at sum outputs of the Ripple Carry Adder until carry propagation is complete.

¨       In synchronous arithmetic units, the allowed time for adder's operation is worst-case delay which is nDFA .

 

Number Systems

    - Conventional Number System

         >Properties

         >Binary, Decimal, Hexadecimal

         >Number Base Conversion

    - Unconventional Number System

         >Roman Number System

         >Signed Digit Number System

         >Binary SD Number System

Fast Addition

    - Half and Full Adders

    - Ripple Carry Adder

    - Carry Look-Ahead Adders

Fast Multiplication

    - Carry Save Adders

    - Additive & Non-additive Multiplier

    - Counters