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U. Glaeser

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Array-Type Multiplier<br />

The simplest parallel multiplier is such that pairs of an AND gate and a 1-bit full adder are laid out<br />

repetitively and connected in sequence to construct an n 2 array [1,22]. An example of a 4 × 4-bit parallel<br />

multiplier to manipulate two positive numbers is shown in Fig. 9.26. The operation time in this multiplier<br />

equals to sum of delays that consist of an AND gate, four FAs, and a 4-bit carry-propagate adder (CPA).<br />

The CPA may be consisted of a 4-bit RCA. It can be easily understood that the reduction process of<br />

partial products to two at each bit position dominates the operation time in this multiplier except for a<br />

CPA delay. Thus, the acceleration of the compression process for the partial product bits at each bit<br />

position is a key to obtain a fast multiplier. For the basic array-type multiplication in Fig. 9.26, this<br />

compression process constitutes ripple carry connection. The worst-case delay of this type is composed<br />

of 2n FA delays. For most recent high-speed data processing systems that deal with wider word than<br />

32 bits, this delay time is too large to be acceptable. Therefore, some kinds of speeding-up mechanisms<br />

FIGURE 9.26 4 × 4-bit array-type multiplier.<br />

© 2002 by CRC Press LLC<br />

b0<br />

b1<br />

b2<br />

b3<br />

c<br />

bj<br />

3,3<br />

a<br />

3<br />

MC MC MC MC<br />

MC MC MC MC<br />

MC MC MC MC<br />

MC MC MC MC<br />

MC<br />

a2 a1 a0<br />

p3,3 c2,3 p2,3 c1,3 p1,3 c0,3<br />

4-bit CPA<br />

z7 z6 z5 z4<br />

pi-1<br />

c i-1,j<br />

FA<br />

ai<br />

c i,j pi,j<br />

z0<br />

z1<br />

z2<br />

z3<br />

0

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