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Example 1: (4517) - (260) 8 +1 +1
8
Answer: 7’s complement of 0260 is 7517 4 5 1 7
8’s complement of 7517 is 7520 + 7 5 2 0
Adding 4517 and 7520, we get 1 4 2 3 7
Discarding MSB 1, we get 4237
(4237)
8
Example 2: (757.76) - (51.77) 8 +1 +1 +1
8
Answer: 7’s complement of 051.77 is 726.00 7 5 7 . 7 6
8’s complement of 726.00 is 726.01 + 7 2 6 . 0 1
Adding 757.76 and 726.01, we get 1 7 0 5 . 7 7
(705.77) 8 Dropping leftmost 1, we get 705.77
Example 3: (360) - (4567) 8 3 6 0
8
Answer: 7’s complement of 4567 is 3210. + 3 2 1 1
8’s complement of 3210 is 3211 3 5 7 1
Adding 360 and 3211, we get 7’s complement is 4206
8’s complement is 4207
(-4207) 8
Example 4: (55.22) - (457.76) 8 5 5 . 2 2
8
Answer: 7’s complement of 457.76 is 320.01 + 3 2 0 . 0 2
3 7 5 2 4
8’s complement of 320.01 is 320.02 7’s complement is 402.53
Adding 55.22 and 320.02, we get 8’s complement is 402.54
(-402.54) 8
1.5 HEXADECIMAL ARITHMETIC
Like other number systems, the arithmetic of hexadecimal numbers involves hexadecimal addition, hexadecimal
subtraction, hexadecimal multiplication, and hexadecimal division. Hexadecimal arithmetic operations start from the
rightmost least significant bit.
1.5.1 Hexadecimal Addition
Hexadecimal addition can be done by following steps:
1. Sum of the digits of the addends are calculated starting from the rightmost digit to the leftmost.
2. If the sum is less than 16, write the hexadecimal value as the result in that column.
3. If the sum exceeds 15, then subtract 16 from the result. The difference is taken as sum and 1 is carried to the next
more significant column.
Note: Alternatively, hexadecimal addition can be done using hexadecimal addition table. Add row value
with column value. The intersection cell is the sum. If the result is 2-digit, then the right digit is taken as
sum and left digit 1 is carry to the adjacent left digit.
3232 Touchpad Computer Science-XI

