Respuesta :
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
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
