You are given a 11-bit floating point representation with 1-sign bit, 3 bits for the exponent, and 7-bits for the mantissa. express 15.75 in this representation

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

sign bit -   Exponent -     Mantissa

The representation of 15.75 in binary in 11 bits is given as

0 - 111 - 1111 11 0

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

15 in decimal = 1111 in binary

2.

Now convert 0.75 by dividing 2 ,

multiplying = integer + fractional part;

1) 0.75 × 2 =  1.5 = 1 + 0.5;

2) 0.5 × 2 = 1= 1 + 0;

so

0.75 in decimal = 0.11 in binary

3. Because it is the 15.75 is positive number so we add 0 in extreme right as

15.75 =  0  1111 . 11

4.  Now making it normalize as by moving point

0.1111 11 x 2^4

so exponent is 4.

5. As exponent is 3 bits

exponent + 2^ (No of bits-1) -1

4+ 2 ^ (3-1) - 1 =  4+4 -1 = 8-1 = 7

Now divide 7 by 2

so

7/2 = 3 (Quotient)     and 1 (remainder)

3/2 = 1 (Quotient)     and 1 (remainder)

so exponent in bits is 111

6. Now calculate mantissa

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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