6 Transmission-Gate Adder (1) A = 1 => -A = 0 => TG is open => out = -B A = 0 => -A = 1 => TG is closed => out = B A = 1 => -A = 0 => TG is closed => out = B A = 0 => -A = 1 => TG is open => out = -B TG XOR TG XNOR
12 Carry-Look-Ahead Adder – CLA (1) Idea: speed up carry computation – C i+1 = G i + P i* C i Propagate: P i = A i + B i if P i = 1, then carry from (i-1)th stage is propagated Generate: G i = A i *B i if G i = 1 there is carry out
17 Brent-Kung CLA a) lookahead terms b) CLG cell c) cells can be rearranged into tree d) simplified representations for part a) e) simplified representation for part c) f) lookahead logic for 8-bit adder g) Brent-Kung adder Reduces delay, increases the regularity, reduces the number of unnecessary switching events (power)
24 Carry Skip Adder: Motivation Computing P 3-0 is much simpler than computing G 0-3 Let’s compute only P 3-0 !
25 Carry Skip Adder Carries begin rippling simultaneously through each block; If any block generates a carry, then the carry out will be true, even the carry-in may not be not true yet. If at the start of each add operation the carry-in to each block is 0, then correct carry-outs will be generated – carry-out can be thought of as if it is the G signal Practical only if the carry-in signals can be easily cleared at the start of each operation – e.g. precharging CMOS
26 Carry Skip Adder: Analysis Assume it takes 1 time unit for signal to propagate through two logic level n bits wide adder blocks of size k It will take k units for a carry to ripple through a block of size k Critical path k units for the first block n/k – 2 units to skip the blocks k units to ripple through the last block Increase the efficiency by varying the blocks size 20 bits (4, 4, 4, 4, 4,): Delay = 4 + 3 + 4 = 11 20 bits (2, 5, 6, 5, 2): Delay = 9
29 Conditional Sum Adder (3) A00101101 B10110110 0Si 0 100110110 Ci 0 00100100 Si 1 011001001 Ci 1 10111111 1Si 0 100100110 Ci 0 0110 Si 1 111001001 Ci 1 0111 2Si 0 110100110 Ci 0 01 Si 1 111001001 Ci 1 011 3S0S0 111000110 0 S1S1 111001001 0
30 Hybrid Designs: An Example Combine CLA (Carry Look-Ahead) with RCA
Your consent to our cookies if you continue to use this website.