Page 33 - ComputerScience_Class_11

Example 2: (111.1) - (11000.10) (using 2’s complement method).
2
2
Answer: 1’s complement of 11000.10 is 00111.01. +1 +1 +1 +1
1 1 1 . 1
2’s complement = 00111.10 + 0 0 1 1 1 . 1 0
Adding 111.1 and 00111.10, we get 01111.00 0 1 1 1 1 . 0 0

(-10001.00) 2 1’s complement of 01111.00 is 10000.11
2’s complement of 10000.11 is 10001.00
1.3.3 Binary Multiplication
Binary numbers are multiplied in the same manner as decimal numbers. When two binary numbers are multiplied, for
each digit of the second number, the product of that digit and the first binary number is calculated.

Then, it is shifted 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.

X Y X × Y
0 0 0 × 0 = 0
0 1 0 × 1 = 0

1 0 1 × 0 = 0
1 1 1 × 1 = 1

Steps for Binary 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 the rules of binary multiplication, starting from the
rightmost bit to the leftmost bit. Shift one bit to the left after each multiplication.
3. Add the results using binary addition rules.
Example 1: Perform the following binary multiplication (1001) × (110) 2
2
Answer: 1 0 0 1
x 1 1 0
0 0 0 0
1 0 0 1 x
+ 1 0 0 1 x x

1 1 0 1 1 0
(110110) 2
Example 2: Perform the following binary multiplication (11101) × (1101) 2
2
Answer: 1 1 1 0 1
x 1 1 0 1
+1 +1 +1 +1 +1 +1
1 1 1 0 1
0 0 0 0 0 x
1 1 1 0 1 x x
+ 1 1 1 0 1 x x x
1 0 1 1 1 1 0 0 1

(101111001) 2

System of Numeration 31