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356 CHAPTER 8 / ARITHMETIC DEVICES AND ARITHMETIC LOGIC UNITS (ALUs)

0(H) 0(H) 0(H)

A 0(H) A B m R > A B in R > A B in R Ro(H)
0(H) B 0(H) B B 0 (H) B
S E 'out S £ S £ oul
1
i r r i
Mm A ! A E „ A £
£Jn R
^ m R
0(H) - B B 0(H)~ B B,(H)- B
v_ S t S E
S E 'out out
r i r ir
A 2 (H)- A E 'm R . A E 'fci R > A E 'in R — R 2 (H)
B 0 (H)~ B B,(H)- B B 2(H)- B
S E out I S E o*_ S E oul

T r i r r
A 3 (H)- A E . A E } [n R „ A E m R
A B B ;
B,(H)- B B 2(H)- B 0(H)- B
00 0 0 0
£
S E out i S u S E out 0 0 1 1 1
0 1 0 1 1
r r
'
A 4 (H)- A E in R , A E „ A fi n R — R 4(H) 0 1 1 1 0
B 2 (H)- B 0(H)- B 0(H)- B 1 0 0 0 1
4 s < 1 1 0 1 0 0
B OHl S B out
1 1 0 0 0
tf? ife ? 1 1 1 1 1
J J J
Q 2(L) = Q 2(H) Q 1(L) = Q,(H) Q 0(L) = Q 0(H)
*
(b)
FIGURE 8.23
(a) Parallel divider for a 5-bit dividend, A, 3-bit divisor, B, a 3-bit quotient, Q, and a 5-bit remainder,
R, designed with an array of 15 subtracter modules of the type shown in Fig. 8.22. (b) Truth table for
a full subtracter.

The divider in Fig. 8.23 can be expanded to accommodate larger dividends and quotients
by adding subtracter modules in both the 7- and X-directions, respectively. Referring to
Fig. 8.20, the relationship between n, m, and k is given by
k = n-m + l (8.12)

for full usage of an n x k array of subtracter modules. For example, a 16-bit dividend
(n = 16) and an 8-bit divisor (m = 8) can be used to generate a 9-bit quotient (k = 9) in a
16x9 array of subtracter modules. Or a 32-bit dividend and a 24-bit divisor can be used
to generate a 9-bit quotient in a 32 x 9 array of subtracter modules. In all such cases the
remainder is of n bits. It is also acceptable to use any lesser portion of a given array of
subtracter modules to carry out a divide operation, but Eq. (8.12) must still apply to that