Type of Adders

Type of Adders - 1. RippleCarryAdder The ripple carry adder...

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b a p = b a g = i i C p C b a S = = i o C p g C + = 3 2 1 0 * p p p p P = 0 1 2 3 1 2 3 2 3 3 * g p p p g p p g p g G + + + = in out C P G C + = * * i i i i i i b a t b a p + = = 1. Ripple Carry Adder The ripple carry adder is composed of a chain of full adders with length n, where n is the length of the input operands. 1.1 Full Adder The following Boolean expressions describe the full adder. and Equation 1 where a and b are the input operands and p and g are the propagate and generate signals respectively. Carry is propagated if p is high or is generated if g is high. Thus, the sum S and carryout C o signals can be expressed as: and Equation 2 where C i is the carry-in signal. 2. Carry Look-ahead Adder Weinberger and Smith proposed this scheme in 1958 [1]. It uses look-ahead technique rather than carry-rippling technique to speed-up the carry propagation. By using additional logics, group generate and propagate signals can be generated. Equation 33, Equation 34 and Equation 35 show the logical expression of prefix-4 group generate, propagate and carry-out signals respectively. Thus, multiple levels of carry-lookahead logics can be used to propagate carry-in from the least significant bit (LSB) to the most significant bit (MSB). Equation 3 Equation 4 Equation 5 3.  Ling Adder Adder proposed by Ling is an improved version of conventional carry-lookahead adder [6]. This approach is faster and less expensive. It replaces the conventional propagate operator from a XOR with an OR gate which results in a much cheaper operation. Equation 6 Rather than propagating the carry G i as conventional carry-lookahead technique do, Ling’s approach replaces G i by H i , where
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1 - + = i i i G G H ( 29 ( 29 ( 29 Ling H t g H G t g G p g g G p G g g G al convention G p g G i i i i i i i i i i i i i i i i i i i i i 1 1 1 1 1 1 1 - - - - - - - + = + = + + = + + = + = ( 29 ( 29 Ling g t t g t g g g t t t g t t g t g H al convention g t t t g t t g t g G 0 1 2 1 2 2 3 0 0 1 2 1 1 2 2 2 3 0 1 2 3 1 2 3 2 3 3 * * + + + + + + = + + + = G r G r- 1 ...
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This note was uploaded on 11/02/2010 for the course EE 3193 taught by Professor Halenlee during the Spring '10 term at NYU Poly.

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Type of Adders - 1. RippleCarryAdder The ripple carry adder...

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