Page 37 - ComputerScience_Class_11

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 14237 1 4 2 3 7

(4237) 8 Discarding MSB 1, we get 4237
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 1705.77 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 3571 7’s complement is 4206

(-4207) 8 8’s complement is 4207

Example 4: (55.22) - (457.76) 8
8
Answer: 7’s complement of 457.76 is 320.01 5 5 . 2 2
8’s complement of 320.01 is 320.02 + 3 2 0 . 0 2
.
3
7
5
Adding 55.22 and 320.02, we get 375.24 7’s complement is 402.53 2 4
(-402.54) 8 8’s complement is 402.54
1.4.3 Octal Multiplication
It is the process of multiplying octal numbers digit by digit, similar to decimal multiplication. However, if the product is
8 or more, it is converted to its octal equivalent using the division method.

Rules of Octal Multiplication are:
1. Write the multiplicand and multiplier one below the other, aligning their digits from right to left.
2. Multiply each bit of the multiplicand and multiplier using rules of Octal multiplication, starting from the right most
bit to the leftmost bit. The red bit of each result in the table is the carry. Shift one bit to left after each multiplication.
3. Add results using octal addition rules.

x 0 1 2 3 4 5 6 7
0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7

2 0 2 4 6 10 12 14 16
3 0 3 6 11 14 17 22 25
4 0 4 10 14 20 24 30 34

5 0 5 12 17 24 31 36 43
6 0 6 14 22 30 36 44 52
7 0 7 16 25 34 43 52 61

System of Numeration 35