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1. Design and Implementation of VLSI Systems
(EN1600)
Lecture 26: Datapath Subsystems 2/4

2. Last lecture we designed a carry-ripple
adder
PG summary
• For a full adder, define what happens to carry
– Generate: Cout = 1 independent of C
• G=A•B
– Propagate: Cout = C
• P=A⊕B
– Kill: Cout = 0 independent of C
• K = ~A • ~B

3. Group carry calculations
i k k-1 j
The carry into bit i is the carry-out of bit i-1
The sum is equal to

4. Group generate
i k k-1 j

5. Carry-ripple adder revisited
A4 B4 A3 B3 A2 B2 A1 B1 Cin
1: Bitwise PG logic
G4 P4 G3 P3 G2 P2 G1 P1 G0 P0
2: Group PG logic
G3:0 G2:0 G1:0 G0:0
C3 C2 C1 C0
3: Sum logic
C4
Cout S4 S3 S2 S1

6. Carry-ripple adder revisited
A4 B4 A3 B3 A2 B2 A1 B1 Cin
G4 P4 G3 P3 G2 P2 G1 P1 G0 P0
G3:0 G2:0 G1:0 G0:0
C3 C2 C1 C0
C4
Cout S4 S3 S2 S1
The critical path now proceeds through a chain of AND-OR
gates rather than a chain of majority gates

7. 8-bit adder/subtractor
add/subt C0=Cin
 Subtraction – complement A0 1-bit
all subtrahend bits (xor FA S0
gates) and set the low B0 C1
order carry-in A1 1-bit
FA S1
B1
C2
A2 1-bit
FA S2
B2 C3
...
C7
A7 1-bit
FA S7
B7
C8=Cout