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2.9 BINARY ARITHMETIC 61
Consider the following simple example for the division operation, which will be carried
out in both decimal and binary:
DD_ _ r0.375"| _ ro.011"|
~ ~
EXAMPLE 2.31 In decimal:
a = 1 - D s = 0.5
k Q = 1 +a = 1.5
D sk Q = 0.75
*i = l + (0.75)ioc = 1.25
D skoki = 0.9375.
k 2 = 1 + (0.9375) ioc = 1-0625
D sk 0kik 2 = 0.99609375
fc 3 = 1 + (0.99609375) 10C = 1.00390625
D sk 0kik 2k3 = 0.999984741.
Therefore, after four iterations the quotient becomes
Q = D Dk 0kik 2ki =0.749988556
6
~
= 0.749989 rounded to six places (10~).
Note that a fifth iteration with Jk 4 = 1.000015259 produces Q = 0.750000 rounded to
six places.
In binary:
a = l -D 5 = 0.1
k Q = l+a = 1.1
1+(0.11) 2 C = 1.01
=0.1111
= 1-0001
= 1.00000001
= 0.1111111111111111.
