Answer:
Sign Bit = 0 (for Positive number)
Exponent = 111 (Three Bit) calculated in step 5
Mantissa = 1111 11 0 (7 bits for mantissa)
the answer is
<em>sign bit - Exponent - Mantissa</em>
The representation of 15.75 in binary in 11 bits is given as
<em>0 - 111 - 1111 11 0</em>
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Explanation:
Given data
15.75 in decimal
calculate it in binary.
1.
15/2 = 7 (Quotient) and 1 (remainder)
7/2 = 3 (Quotient) and 1 (remainder)
3/2 = 1 (Quotient) and 1 (remainder)
by arranging them in order
<em>15 in decimal = 1111 in binary</em>
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<em>2.</em>
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<em>Now convert 0.75 by dividing 2 , </em>
multiplying = integer + fractional part;
1) 0.75 × 2 = 1.5 = <em><u>1</u></em> + 0.5;
2) 0.5 × 2 = 1= <u><em>1 </em></u>+ 0;
<em>so</em>
<em>0.75 in decimal = 0.11 in binary</em>
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<em>3. </em>Because it is the 15.75 is positive number so we add 0 in extreme right as
<em> 15.75 = 0 1111 . 11</em>
<em>4. Now making it normalize as by moving point</em>
<em />
0.1111 11 x 2^4
so exponent is 4.
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<em>5. As exponent is 3 bits </em>
exponent + 2^ (No of bits-1) -1
4+ 2 ^ (3-1) - 1 = 4+4 -1 = 8-1 = 7
Now divide 7 by 2
<em>so </em>
7/2 = 3 (Quotient) and 1 (remainder)
3/2 = 1 (Quotient) and 1 (remainder)
<em>so exponent in bits is 111</em>
<em>6. Now calculate mantissa</em>
Just remove the point from 0.1111 11 as 1111 11
Now add rest of the bits 0 at right side
mantissa = 1111 11 0
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