1. Design and Implementation of VLSI Systems (EN1600) Lecture 27: Datapath Subsystems 3/4 Prof. Sherief Reda Division of Engineering, Brown University Spring 2008 [sources: Weste/Addison Wesley – Rabaey/Pearson]

2. Manchester carry adder Using transmission gates Using dynamic gates

3. Manchester carry chains Critical path involves a series propagate transistor for each bit  a significant over carry-ripple (which used majority or AND-OR gate)

4. Equivalence circuits for Manchester carry chain

5. Carry skip adder If (P 0 & P 1 & P 2 & P 3 = 1) then C o,3 = C i,0 otherwise the block itself kills or generates the carry internally A0A0 B0B0 S0S0 C i,0 FA A1A1 B1B1 S1S1 A2A2 B2B2 S2S2 A3A3 B3B3 S3S3 C o,3 BP = P 0 P 1 P 2 P 3 “Block Propagate”

6. Carry-skip adder Carry-ripple is slow through all N stages Carry-skip allows carry to skip over groups of n bits –Decision based on n-bit propagate signal Original design by Charles Babbage

7. Carry-lookahead adder Similar to the carry-skip adder, but computes generate signals as well as group propagate signals to avoid waiting for a ripple to determine if the group generates a carry.

8. Carry-select adder One adder calculates the sums assuming a carry-n of 0 while the other calculates the sums assuming a carry-in of 1. The actual carry triggers a multiplexer that chooses the appropriate sum

9. II. Comparators A.0’s detector and 1’s detectors B.Equality comparator:A = B C.Magnitude comparator:A < B

10. A. 1’s and 0’s detectors 1’s detector: N-input AND gate 0’s detector: NOTs + 1’s detector (N-input NOR) When is this circuit structure a good idea?

11. B. Equality comparator Check if each bit is equal (XNOR, aka equality gate) 1’s detect on bitwise equality

12. C. Magnitude comparator  Compute B-A and look at sign  B-A = B + ~A + 1  For unsigned numbers, carry out is sign bit