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Unformatted text preview: traction method. For example,
35 -f 5 may be thought of as:
35-5 = 30
30-5 = 25 25-5 = 20
20-5 = 15
15-5 = 10
10-5 = 5
5-5 = 0
That is, the divisor is subtracted repeatedly from the dividend until the result of
subtraction becomes less than or equal to zero. The total number of times subtraction was
performed gives the value of the quotient. In this case, the value of quotient is 7 because
the divisor (5) has been subtracted 7 times from the dividend (35) until the result of
subtraction becomes zero. If the result of last subtraction is zero, then there is no
remainder for the division. But, if it is less than zero, then the last subtraction is ignored
and the result of the previous subtraction is taken as the value of the remainder. In this
case, the last subtraction operation is not counted for evaluating the value of the quotient.
The process is illustrated below with an example.
Divide 3310 by 610 using the method of addition.
33-6 = 27
27-6 = 21
3 - 6 = -3
Total number of subtractions = 6. Since the result of the last subtraction is less than zero,
Quotient = 6-1 (ignore last subtraction) = 5 Remainder = 3 (result of previous
Hence, 33 ÷ 6 = 5 with a remainder 3.
Note that it has been assumed here that all the subtraction operations are carried out using
the complementary subtraction method (additive method).
Once again, performing division inside a computer by the way of addition is desirable
because the addition and complementation operations are easily performed in a computer
and usually save the labour and expense of designing complicated circuits.
We have demonstrated how computer arithmetic is based on addition. Exactly how this
simplifies matter can only be understood in the context of binary (not in decimal). The
number of individual steps may indeed be increased because all computer arithmetic is
reduced to addition, but the computer can carry out binary additions at such great speed
that this is not a disadvantage.
Points to Remember
Almost all computers use binary numb...
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This document was uploaded on 04/07/2014.
- Spring '14