Binary Arithmetic
DIVISION
Shift & Subtract
With the advent of calculators, most people don’t use the long division method anymore. Calculators are not permitted in the HSC exam so you will need to brush up on the old steam driven method of division.
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quotient r remainder |
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divisor |
dividend |
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remainder |
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Look at some worked examples.
Example 1
1100011 ¸ 1001
Draw up the long division. The coloured vertical lines are to remind you to keep your working neat.
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There are four digits in the divisor 1001. Write these directly under the first four digits of the dividend.
The divisor needs to be less than the digits above so that you can do the subtraction.
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1100>1001 so you can do the subtraction and place 1 in the quotient line.
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Bring down the next digit of the dividend. Since 1001>110 write 0 in the quotient line
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Bring down the next digit of the dividend.
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1101>1001 so do the subtraction and put 1 in the quotient line.
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Bring down the next digit of the dividend.
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Since both numbers are the same the subtraction can be done leaving a remainder of 0
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So the answer is
1100011¸1001=1011r0
Example 2
1000001¸101
In this case the divisor was greater than the first three digits of the dividend so the divisor was divided into the first four digits.
This means that the 1 in the quotient line appears above the fourth digit
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Example 3
This is an example that produces a remainder
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