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column to the left. It is important to note here that the value borrowed depends upon the
base of the number and is always the decimal equivalent of the base. Thus, in decimal, 10
is borrowed; in binary, 2 is borrowed; in octal, 8 is borrowed; in hexadecimal, 16 is
borrowed. The second step is simply to subtract the lower value from the upper value.
The complete table for binary subtraction is as follows:64
00=0
10=1
11=0
0  1 = 1 with a borrow from the next column . Observe that the only case in which it is necessary to borrow is when 1 is subtracted from
0. The exact procedure is illustrated with the examples given below.
Example 5.4.
Subtract
011102froml01012
Solution:
Borrow 12
0202
10101
01110
00111 In the first column, 0 is subtracted from 1. No borrow is required in this case and the
result is 1. In the second column, we have to subtract 1 from 0. As seen in the table for binary subtraction, a borrow is necessary to perform this subtraction. Hence, a 1 is
borrowed from the third column, which becomes 2 in the second column because the
base is 2. A 1 in the 4s column is equal to 2 in the 2s column. Now, in the second
column, we subtract 1 from 2 giving a result of 1. The borrow performed in the second
column reduces the 1 in the third column to 0. Hence, in the third column, once again we
have to subtract 1 from 0 for which borrow is required. The fourth column contains a 0
and thus has nothing to borrow. Therefore, we have to borrow from the fifth column.
Borrowing 1 from the fifth column gives 2 in the fourth column. A 1 in the 16s column
equals 2 in the 8s column. Now the fourth column has something to borrow. When 1 of
the 2 in the fourth column is borrowed, it becomes 2 in the third column. Now, in the
third column, we subtract 1 from 2 giving a result of 1. The borrow performed in the third
column reduces the 1 in the fifth column to 0 and the 2 in the fourth column to 1. Hence,
subtraction of the fourth column is now 1 from 1, giving 0 and in the fifth column,
subtraction is 0 from 0, giving 0. Thus the final result of subtraction is 00111 2. The result
may be verified by subtracti...
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 Spring '14

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