Instead of thinking of an adder as a device that adds two numbers and then links the carries together, we can think of the adder as a hardware device that can add three inputs together (ai, bi, ci) and produce two outputs (s, ci + 1). When adding two numbers together, there is little we can do with this observation. When we are adding more than two operands, it is possible to reduce the cost of the carry. The idea is to form two independent sums, called S' (sum bits) and C' (carry bits). At the end of the process, we need to add C' and S' together using a normal adder. This technique of delaying carry propagation until the end of a sum of numbers is called carry save addition. The block drawing on the lower right of Figure B.14.1 (see below) shows the organization, with two levels of carry save adders connected by a single normal adder. Calculate the delays to add four 16-bit numbers using full carry-lookahead adders versus carry save with a carry-lookahead adder forming the final sum.

Figure B.14.1

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a3 b3 a2 b2 a1 b1 a0 b0 A B E F + + Traditional adder e3 e2 e1 e0 + Traditional adder f3 f2 f1 fo Traditional adder + s5 s4 s3 s2 s1 s0 b3 e3 f3 b2 e2 12 b1 et f1 b0 e0 fo A B F Carry save adder a3 a2 Carry save adder s'4 c'3 s'3c2, s'2 c'1, s'1 c'o s'0 Traditional adder + s5 s4 s3 s2 s1 s0 + +