Basic Addition Review Basic Adders and the Carry Problem Carry Propagation Speedup Speed/Cost Tradeoffs Two-operand Versus Multi-operand Adders.

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Presentation transcript:

Basic Addition Review Basic Adders and the Carry Problem Carry Propagation Speedup Speed/Cost Tradeoffs Two-operand Versus Multi-operand Adders

Half Adders

Adder Equations

Full Adder F (A,B,C) = A  B  C G = AB + AC + BC AB S CiCo Cin AB Cout Sum Sum = A  B  Cin Cout = AB + Cin A + Cin B = AB + Cin (A + B) Full Adder (FA)

4-Bit Ripple Carry Adder AB S CiCo AB S CiCo AB S CiCo AB S CiCo Cin A(0) Cout B(0)A(1)B(1)A(2)B(2)A(3)B(3) C(0)C(1)C(2)C(3)C(4) Sum(0)Sum(1)Sum(2)Sum(3) A[3:0] B[3:0] SUM[3:0] + C[0] C[4]

Full Adder Implementations

Adder Circuits Using FA

Ripple Carry Adder Layout

Delay in Ripple Adder

Adders as Logic Elements

Adder Exceptions

Adder Exception Circuitry

Carry Propagation Analysis

Carry Completion Detection

Counters

Asynchronous up-Counter

Three-stage up-Counter

Generate, Propagate and Kill

Transfer Signal

Manchester Carry Chain