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Basic Addition Review Basic Adders and the Carry Problem

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Presentation on theme: "Basic Addition Review Basic Adders and the Carry Problem"— Presentation transcript:

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

2 Half Adders

3 Adder Equations

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

5 4-Bit Ripple Carry Adder
S Ci Co A B S Ci Co A B S Ci Co A B S Ci Co Cout C(4) C(3) C(2) C(1) C(0) Cin Sum(3) Sum(2) Sum(1) Sum(0) A[3:0] B[3:0] + C[4] C[0] SUM[3:0]

6 Full Adder Implementations

7 Ripple Carry Adder Layout

8 28T Full Adder Implementation

9 4-Bit Adder Reduced Ripple Delay

10 24T Full Adder Implementations

11 Adder Circuits Using FA

12 Delay in Ripple Adder

13 Adders as Logic Elements

14 Adder Exceptions

15 Adder Exception Circuitry

16 Carry Propagation Analysis

17 Carry Propagation Analysis

18 Carry Completion Detection

19 Counters

20 Asynchronous up-Counter

21 Three-stage up-Counter

22 Generate, Propagate and Kill

23 Transfer Signal

24 Manchester Carry Chain

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