Page 31 - computer science (868) class 11
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leftwards so that its rightmost digit lines up with the digit in the second number that was used. The sum of all these
partial products gives the result. The following rules are followed to multiply two binary numbers.
1 0 1 0
X Y X × Y
1 0 1
0 0 0 × 0 = 0 1 0 1 0
0 1 0 × 1 = 0 0 0 0 0 ×
1 0 1 × 0 = 0 1 0 1 0 × ×
1 1 1 × 1 = 1 1 1 0 0 1 0
For example, let us multiply (1010) by (101) .
2
2
1.3.4 Binary Division
1 0 1 Quotient
Binary numbers are also divided in a manner similar to decimal
numbers. The division is done by the repeated process of 101 1 1 0 1 1
subtraction. In binary division, the following rules are followed: 1 0 1
0 / 1 = 0 1 1 1
1 / 1 = 1
1 0 1
For example, let us divide (11011) by (101) .
2 2
1 0 Remainder
1.4 OCTAL ARITHMETIC
The arithmetic of octal numbers involves octal addition, octal subtraction, octal multiplication, and octal division. Octal
arithmetic operations start from its rightmost least significant bit.
1.4.1 Octal Addition
The steps to be followed are:
1. The sum of the digits of the addends is calculated starting from the rightmost digit to the leftmost.
2. If the sum is less than 8, write the octal value as the result in that column.
3. If the sum exceeds 7, then subtract 8 from the result. The difference is taken as sum and 1 is carried to the next more
significant column.
+ 0 1 2 3 4 5 6 7
0 0 1 2 3 4 5 6 7
1 1 2 3 4 5 6 7 10
2 2 3 4 5 6 7 10 11
3 3 4 5 6 7 10 11 12
4 4 5 6 7 10 11 12 13
5 5 6 7 10 11 12 13 14
6 6 7 10 11 12 13 14 15
7 7 10 11 12 13 14 15 16
Note: An addition table for octal numbers can also be used to do the same. Add row value with column
value. The intersection cell is the sum. If it is greater than 7, then the right digit is taken as sum and 1 is
carry to the previous digit the next more significant column.
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