Page 21 - computer science (868) class 11
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Example 2: Convert (215.125) to octal.
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Answer: Integer part Fractional part
Divisor Dividend Remainder Multiplication Result Integer part
8 215 0.125 x 8 = 1.000 1
8 26 7
8 3 2
0 3
(215.25) = (327.1) 8
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1.2.3 Decimal to Hexadecimal
The steps to be followed are:
1. Divide the number by 16 and the quotient becomes the new number (dividend).
2. Store the remainder of the division separately.
3. Repeat steps 1 & 2 until new number = 0.
4. Arrange the remainders from the bottom (LSD) to top (MSD) to get the result.
5. For the decimal part, repeat step 6 until the fractional part becomes 0 or till four places after decimal.
6. Multiply the fractional part by 16 and store the integer part of the product separately.
7. Arrange the binary digits of the integer part from top to bottom for the result of the fractional part.
A similar procedure as illustrated in decimal to binary conversion is followed with 16.
Example 1: Convert (740) to hexadecimal.
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Answer: Integer part
Divisor Dividend Remainder
16 740
16 46 4
16 2 E
0 2
(740) = (2E4)
10 16
Example 2: Convert (215.125) to hexadecimal.
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Answer: Integer part Fractional part
Divisor Dividend Remainder Multiplication Result Integer part
16 215
0.125 x 16 = 2.0 2
16 13 7
0 D
(215.25) = (D7.2) 16
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1.2.4 Binary to Decimal
The steps to be followed are:
1. Multiply each binary digit with its corresponding 2 place value starting from right to left (LSB to MSB).
2. Add each product term to get the final result.
3. The place value of the integer part starts from 0 and increases by 1 as we move left.
4. The place value of the fractional part starts from -1 and decreases by 1 as we move right.
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