Page 29 - ComputerScience_Class_11

3
2
0
1
8 (2 ) 4 (2 ) 2 (2 ) 1 (2 ) Hexa
0001 1001 0001 . 0001 0 0 0 1 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 1
1 9 1 . 1 1 0 0 1 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 9
0 0 0 1 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 1
(191.1) 16 0 0 0 1 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 1

Example 3: Convert (25C9) to octal.
16
Answer: Converting Octal to Binary first 8 (2 ) 4 (2 ) 2 (2 ) 1 (2 ) Hexa
2
3
0
1
2 5 C(12) 9 0 0 1 0 0 x 8 + 0 x 4 + 1 x 2 + 0 x 1 = 2
0010 0101 1100 1001 0 1 0 1 0 x 8 + 1 x 4 + 0 x 2 + 1 x 1 = 5
Binary equivalent is (0010010111001001) 2 1 1 0 0 1 x 8 + 1 x 4 + 0 x 2 + 0 x 1 = 12
Grouping 3 bits, we get 010 010 111 001 001 1 0 0 1 1 x 8 + 0 x 4 + 0 x 2 + 1 x 1 = 9
Converting to Octal

010 010 111 001 001 4 (2 ) 2 (2 ) 1 (2 ) Octal
1
0
2
2 2 7 1 1 0 1 0 0 × 4 + 1 × 2 + 0 × 1 = 2
0 1 0 0 × 4 + 1 × 2 + 0 × 1 = 2
1 1 1 1 × 4 + 1 × 2 + 1 × 1 = 7
(22711) 8 0 0 1 0 × 4 + 0 × 2 + 1 × 1 = 1
0 0 1 0 × 4 + 0 × 2 + 1 × 1 = 1

1.3 BINARY ARITHMETIC
The arithmetic of binary numbers involves binary addition, binary subtraction, binary multiplication and binary division.
Like decimal arithmetic, binary arithmetic operations start from the rightmost least significant bit (LSB).

1.3.1 Binary Addition
The basic cases for binary addition are:

Bits Sum Carry
0 + 0 0 0
0 + 1 1 0

1 + 0 1 0
1 + 1 0 1 Added to the adjacent left bits

1 + 1 + 1 1 1 Added to the adjacent left bits

Let us understand with some examples.
Example 1: (1100111) + (11101) 2
2
Answer: +1 +1 +1 +1 +1 +1 +1
1 1 0 0 1 1 1
+ 1 1 1 0 1
1 0 0 0 0 1 0 0

(10000100) 2

System of Numeration 27