Question

1. Represent following floating-point numbers in IEEE single-precision (32-bit) format: a. -0.1875, b. 0.46875

2. What is the decimal value of the following IEEE single-precision (32-bit) floating-point numbers (which are shown in hexadecimal)? a. 3F400000, b. BE000000

Answer 1

1)
a)
-0.1875 in simple binary => .0011
so, -0.1875 in normal binary is .0011 => 1.1 * 2^-3

single precision:
--------------------
sign bit is 1(-ve)
exp bits are (127-3=124) => 01111100
frac bits are 10000000000000000000000

so, -0.1875 in single-precision format is 1 01111100 10000000000000000000000
in hexadecimal it is 0xBE400000

b)
0.46875 in simple binary => .01111
so, 0.46875 in normal binary is .01111 => 1.111 * 2^-2

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127-2=125) => 01111101
frac bits are 11100000000000000000000

so, 0.46875 in single-precision format is 0 01111101 11100000000000000000000
in hexadecimal it is 0x3EF00000

2)
a)
0x3F400000
0 01111110 10000000000000000000000

sign bit is 0(+ve)
exp bits are 01111110 => in decimal it is 126
so, exponent/bias is 126-127 = -1
frac bits are 1

Decimal value is 1.1 * 2^-1
1.1 in decimal is 1.5
1.1 * 2^-1 in decimal is 0.75

so, 3F400000 in IEEE-754 single precision format is 0.75
Answer: 0.75

b)
0xBE000000
1 01111100 00000000000000000000000

sign bit is 1(-ve)
exp bits are 01111100 => in decimal it is 124
so, exponent/bias is 124-127 = -3
frac bits are 

Decimal value is 1. * 2^-3
1. in decimal is 1
1. * 2^-3 in decimal is -0.125

so, BE000000 in IEEE-754 single precision format is -0.125
Answer: -0.125