Unformatted text preview: o follows the same general rules as
decimal number system multiplication. However, learning the binary multiplication is a
trivial task because the table for binary multiplication is very short, with only four entries
instead of the 100 necessary for decimal multiplication. The complete table for binary
multiplication is as follows:
0x0=0
0x1=0
1x0=0
1x1=1
The method of binary multiplication is illustrated with the example given below. It is
only necessary to copy the multiplicand if the digit in the multiplier is 1, and to copy all
0s if the digit in the multiplier is a 0. The ease with which each step of the operation is
.performed is apparent.
Example 5.14.
Multiply the binary numbers 1010 and 1001.
Solution:
1010 Multiplicand
x1001 Multiplier 1010 Partial Product
0000 Partial Product
0000 Partial Product
1010 Partial Product
1011010 Final Product
Note that the multiplicand is simply copied when multiplier digit is 1 and when the
multiplier digit is 0, the partial product is only a string of zero's. As in decimal
multiplication, each partial product is shifted one place to the left from the previous
partial product. Finally, all the partial products obtained in this manner are added
according to the binary addition rules to obtain the final product.
In actual practice, whenever a 0 appears in the multiplier, a separate partial product
consisting of a string of zeros need not be generated. Instead, only a left shift will do. As
a result, Example 5.14 may be reduced to
1010
x l00l
1010
1010SS (S = left shift)
1011010
A computer would also follow this procedure in performing multiplication. The result of
this multiplication may be verified by multiplying 10 10 (10102) by 910 (10012), which
produces a result of 9010 (10110102).
It may not be obvious how to handle the addition if the result of the multiplication gives
columns with more than two Is. They can be handled as pairs or by adjusting the column
to which the carry is placed, as shown by Example 5.15.
Example 5.15.
Multiply the binary numbers 1111 and 111. Solution:
1
X 1 1 1
1 1
1 1
1
1 1
1
1 1
1 1 1
1 1 1
1 0...
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This document was uploaded on 04/07/2014.
 Spring '14

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