Question 4.2: Is ripple-carry adder the smallest 32-bit adder?
Is ripple-carry adder the smallest 32-bit adder?
A 32-bit ripple-carry adder uses 32 1-bit adders. One could design a 32-bit serial adder using a single 1-bit full adder. The input numbers are shifted into the adder, one bit at a time, and carry output from addition of each pair of bits is saved in a flip-flop and fed back to the next addition. The hardware illustrated in Figure 4-12 accomplishes this. The delay
of adder will be 32 *(2t_{g}+t_{ff} ), where 2t_{g} is the delay of the one-bit full adder and t_{ff} is the delay of the flip-flop (including set up time). If a flip-flop delay is at least two gate delays, the delay of the 32-bit serial adder will be at least 128t_{g} . The adder hardware is simple; however, there is also the control circuitry needed to generate 32 shift signals. The registers storing the operands must have shift capability as well.
