Unformatted text preview: ng 14 i0 (= 011102) from 21,o (101012) which gives 7,o (=
001112).
Example 5.5.
Subtract 01110002 from 10111002.
Solution:
Borrow 2
1011100
0111000
0100100 The result may be verified by subtracting 56 10 (= 01110002) from 9210 (= 10111002),
which gives 36,0 (= 01001002).
Additive Method of Subtraction
The direct method of subtraction using theborrow concept seems to be easiest when we
perform subtraction with paper and pencil. However when subtraction is implemented by
means of digital components, this method is found to be less efficient than the additive
method of subtraction. It may sound surprising that even subtraction is performed using
an additive method. This method of subtraction by an additive approach is known as
complementary subtraction.
In order to understand complementary subtraction, it is necessary to know what is meant
by the complement of a number. For a number, which has n digits in it, a complement is
defined as the difference between the number and the base raised to the n th power minus
one. The definition is illustrated with the following examples:
Example 5.6. Find the complement of 37
Solution:
Since the number has 2 digits and the
value of base is 10,
(Base)"l = 1021=99
Now 99  37 = 62
Hence, the complement of 3710 = 6210.
Example 5.7.
Find the complement of 6g. Solution:
Since the number has 1 digit and the
value of base is 8,
(Base)n  1 = 81  1 = 710
Also 68 = 610
Now 710  610 = 110 =18 lg
Hence, the complement of 68 = l8.
Example 5.8.
Find the complement of IOIOI2.
Solution:
Since the number has 5 digits and the value of base is 2,
(Base)nl=25l=3110
Alsol01012 = 2110
Now 31io 21io = lO10 = 10102
Hence, the complement of 101012= 010102.
Observe from Example 5.8 that in case of binary numbers, it is not necessary to go
through the usual process of obtaining complement. Instead, when dealing with binary
numbers, a quick way to obtain a number's complement is to transform all its 0's to l's,
and all its l's to 0's. For example, the complement o...
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This document was uploaded on 04/07/2014.
 Spring '14

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