The complete table for binary multiplication is as

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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.

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