Question

Interpret the following IEEE 754 number in decimal:  0 10010011 111000...

Add the previous IEEE 754 number to the following and express the answer in IEEE 754 format: 0 01011010 0111000...

Answer 1

1)
0 10010011 11100000000000000000000
sign bit is 0(+ve)
exp bits are 10010011 => in decimal it is 147
so, exponent/bias is 147-127 = 20
frac bits are 111

Decimal value is 1.111 * 2^20
1.111 in decimal is 1.875
1.111 * 2^20 in decimal is 1966080.0
so, 01001001111100000000000000000000 in IEEE-754 single precision format is 1966080.0
Answer: 1966080.0

2)
0 01011010 01110000000000000000000
sign bit is 0(+ve)
exp bits are 01011010 => in decimal it is 90
so, exponent/bias is 90-127 = -37
frac bits are 0111

Decimal value is 1.0111 * 2^-37
1.0111 in decimal is 1.4375
1.0111 * 2^-37 in decimal is 1.0459189070388675e-11
so, 00101101001110000000000000000000 in IEEE-754 single precision format is 1.0459189070388675e-11
Answer: 1.0459189070388675e-11

add them up
1966080.0 + 1.0459189070388675e-11. This is almost same as 1966080.0

so, Answer is 0 10010011 11100000000000000000000