U. Glaeser

FIGURE 9.16 Binary SRT division.
The basic scheme is shown in Fig. 9.16. Block 1 initializes the algorithm. In steps 3 and 5, Pk is compared
to ±.5. If Pk ≥ .5, in step 4 the quotient digit is set to 1 and Pk+1 = 2Pk − D. If Pk ≤ −.5, in step 6 the quotient
digit is set to 1 and Pk+1 = 2Pk + D. If the value of Pk is between −.5 and .5, step 7 sets Pk+1 = 2Pk. Finally,
step 8 tests whether all bits of the quotient have been formed and goes to step 2 if more need to be
computed. Each pass through steps 2–8 forms one digit of the quotient. As shown on Fig. 9.16, each pass
through steps 2–8 requires one or two comparisons in steps 3 and 5, and may require an addition (in
step 4 or step 6). Thus computing an n-bit quotient will involve up to n additions and from n to 2n
comparisons.
Higher Radix SRT Divider
The higher radix SRT division process is similar to the binary SRT algorithms. Radix 4 is the most
common higher radix SRT division algorithm with either a minimally redundant digit sets of {2, 1, 0, 1, 2}
or the maximally redundant digit sets of {3, 2, 1, 0, 1, 2, 3}.
The operation of the algorithm is similar to
the binary SRT algorithm shown on Fig. 9.16, except that Pk and Q are applied to a look up table or a
programmable logic array (PLA) to determine the quotient digit. A research monograph provides a
detailed treatment of SRT division [18].
Newton–Raphson Divider
A second division technique uses a form of Newton–Raphson iteration to derive a quadratically convergent
approximation to the reciprocal of the divisor which is then multiplied by the dividend to produce
the quotient. In systems which include a fast multiplier, this process is often faster than conventional
division [19].
© 2002 by CRC Press LLC
4. q n-k-1 = -1
P k+1 = 2P k + D
LE
1. P 0 = N
k = -1
2. k = k + 1
3.
P k : .5
5.
LT
P k : -.5
8.
K : n-1
GE
Q = N/D
GE
GT
LT
4. q n-k-1 = 1
P k+1 = 2P k − D
7. q n-k-1 = 0
P k+1 = 2P k