 October 15, 2023
October 15, 2023
October 15, 2023
###### Digital-Logic-Design
October 15, 2023
 Question 548
The decimal floating point number -40.1 represented using IEEE-754 32-bit representation and written in hexadecimal form is
 A 0xC2206000 B 0xC2006666 C 0xC2006000 D 0xC2206666
Question 548 Explanation:
1. Fraction part can be converted into binary form by multiplying it with 2 and taking non fractional part of the product. Take fractional part and multiply again as explained above.
0.1 x 2= 0.2 → 0
0.2 x 2= 0.4 → 0
0.4 x 2= 0.8 → 0
0.8 x 2= 1.6 → 1
0.6 x 2= 1.2 → 1
(0.1)​ 10​ = (0.00011)​ 2
(40)​ 10​ = (101000)​ 2
101000.00011
Normalize the number
1.0100000011 x 2​ 5
Biased exponent= 5+127= 132=(1000 0100)​ 2
Mantissa= 01000000110000000000000
Sign= 1 Question 548 Explanation:
1. Fraction part can be converted into binary form by multiplying it with 2 and taking non fractional part of the product. Take fractional part and multiply again as explained above.
0.1 x 2= 0.2 → 0
0.2 x 2= 0.4 → 0
0.4 x 2= 0.8 → 0
0.8 x 2= 1.6 → 1
0.6 x 2= 1.2 → 1
(0.1)​ 10​ = (0.00011)​ 2
(40)​ 10​ = (101000)​ 2
101000.00011
Normalize the number
1.0100000011 x 2​ 5
Biased exponent= 5+127= 132=(1000 0100)​ 2
Mantissa= 01000000110000000000000
Sign= 1 