Basic Addition

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
A
B
Sum A ? B ? Cin Cout AB Cin A Cin B
AB Cin (A B)
Cin
Cout
Full Adder (FA)
Sum
5
4-Bit Ripple Carry Adder
A(0)
B(0)
A(1)
B(1)
A(2)
B(2)
A(3)
B(3)
Cout
C(0)
C(1)
C(2)
C(3)
C(4)
Cin
Sum(0)
Sum(1)
Sum(2)
Sum(3)
A30
B30
C4
C0
SUM30
6
Full Adder Implementations
7
Ripple Carry Adder Layout
8
28T Full Adder Implementation
9
4-Bit AdderReduced 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