number_system

# This can be easily seen by considering an example say

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Unformatted text preview: 1 0 0 1 As shown below, the addition in column 3 above can be handled in any one of the following two ways: Addition handled as pairs (Column 3) Additive Method of Multiplication Most computers perform multiplication operation by the way of addition only. This can be easily seen by considering an example, say 4x8. The result for this multiplication can be determined by evaluating, with necessary carry overs, 8 + 8 + 8 + 8. That is, the result is obtained simply by adding the digit 8 four times. Similarly, the computer performs all multiplication operations in binary using the additive approach. The idea of repeated addition may seem to be a longer way of doing things, but remember that the computer is well suited to carry out the operations at great speed. The internal circuit design of computer systems is also simplified to a great extent by using this method of multiplication. Division Once again, division in binary number system is very simple. As in the decimal number system (or in any other number system), division by zero is meaningless. Hence, the complete table for binary division is as follows: 0÷1=0 1÷1=1 The division process is performed in a manner similar to decimal division. The rules for binary division are: 1. Start from the left of the dividend. 2. Perform a series of subtractions in which the divisor is subtracted from the dividend. 3. If subtraction is possible, put a 1 in the quotient and subtract the divisor from the corresponding digits of dividend. 4. If subtraction is not possible (divisor greater than remainder), record a 0 in the quotient. 5. Bring down the next digit to add to the remainder digits. Proceed as before in a manner similar to long division. The method is illustrated by Example 5.16. The result may be verified by dividing 33 10 (1000012) by 610 (1102), which gives a quotient of 510 (1012) and a remainder of 310 (112). Additive Method of Division Even division operation is performed inside most computers by the process of addition only. This may again sound surprising, but it is true. The computer performs the division operation essentially by repeating the complementary sub...
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## This document was uploaded on 04/07/2014.

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