Page 61 - Computer Science V2.0 Class 11

So, (0.A6) 16 = (0.648) 10 ≠ (0.65) 10 because while converting (0.65) to a hexadecimal number, we discarded the
10
hexadecimal digits appearing beyond two places after the radix point.
Example 34: Convert (2C1.CF5) to its equivalent decimal number.
16
Note that we retain four decimal digits in each computation if only three significant digits after the decimal point are
required. Thus we may write:

12 = 0.7500
16
15 = 0.0585 (truncate after four digits)
256

5 = 0.0012(truncate after four digits)
4096
12 15 5
So, + + = 0.75 + 0.0585 + 0.0012 = 0.8097 = 0.809 (truncate after three digits)
16 256 4096

Find decimal representation of (0.2) , (0.4) , (0.C) .
16 16 16

Conversion of Fractional Binary Numbers to Octal
To convert a fractional binary number to its equivalent octal number, form groups of three bits, starting from left to
right after the radix point. If the number of bits is not a multiple of three, append the required number of 0s on the
right end. Finally, replace each group of three bits with an equivalent octal digit.
Example 35: Convert (0 .1011) to an equivalent octal number.
2
two 0s added

.1 0 1 1 0 0

5 4
(.1011) = (.54)
2 8
Now, let us convert a binary number with both integer and fractional parts to an equivalent octal number.
Example 36: Convert (110.01) to an equivalent octal number.
2
1 1 0 . 0 1 0

6 2
(110.01) = (6.2)
2 8
Example 37: Convert (110101111.011101110011) to an equivalent octal number.
2
1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1

6 5 7 3 5 6 3

(110101111.011101110011) = (657.3563) 8
2

Find octal representation of (111000.11) (1100110.001010) (111001.000000011) .
2
2,
2,

Number Systems and Encoding Schemes 47