Page 46 - ComputerScience_Class_11

6. Now, for the decimal part, the steps are as follows:
1. Multiply fractional part by 2 and store the integer part of the product separately.
2. Repeat above step until the fractional part becomes 0 or up to 4 places of decimal.
3. Arrange the binary digits of the integer part from top to bottom for the result of the fractional part.
3. Convert (0.425) to:
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a. Binary b. Octal c. Hexadecimal
Ans. a.
Fractional part
Multiplication Result Integer part
0.425 × 2 = 0.850 0
0.850 × 2 = 1.700 1
0.700 × 2 = 1.400 1
0.400 × 2 = 0.800 0
(0.425) = (0.0110) 2
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b.
Fractional part
Multiplication Result Integer part
0.425 × 8 = 3.4 3
0.4 × 8 = 3.2 3
0.2 × 8 = 1.6 1
0.6 × 8 = 4.8 4

(0.425) = (0.3314) 8
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c.
Fractional part
Multiplication Result Integer part
0.425 × 16 = 6.8 6
0.8 × 16 = 12.8 12(C)
0.8 × 16 = 12.8 12(C)
0.8 × 16 = 12.8 12(C)
(0.425) = (0.6CCC) 16
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4. Convert (10111011.1011) to decimal.
2
Ans. 7 6 5 4 3 2 1 0 -1 -2 -3 -4

1 0 1 1 1 0 1 1 . 1 0 1 1
4
6
5
= 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 -4
3
-2
7
-3
-1
2
1
0
= 128 + 32 + 16 + 8 + 2 + 1 + 1/2 + 1/8 + 1/16
= (187.6875) 10
5. Convert (507.26) to decimal.
8
Ans. 2 1 0 -1 -2
5 0 7 . 2 6
-1
= 5 × 8 + 0 × 8 + 7 × 8 + 2 × 8 + 6 × 8 -2
1
2
0
= 320 + 0 + 7 + 1/4 + 3/32
= (327.34375)
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6. Convert (5B7.2C) to decimal.
16
Ans. 2 1 0 -1 -2
5 B(11) 7 . 2 C(12)
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