Question

A Computer uses IEEE-754 single precision format to represent floating points. What value (in decimal) the computer represents if the floating point is represented using the following binary digits. Show all the steps used in finding the answer.

0 01111110 10100000000000000000000

Answer 1

Answer:

0.1825   is the answer

Explanation:

Single precision is 32 bit and double precision is 64 bit.  

Single bit = 0

Exponent (8 bit) = 01111110

Mantissa (23 bits) = 10100000000000000000000

We must calculate using below formla,

x = [-1]^s * (1 + Fraction) * 2^(Exponent-bias)

i) Left most bit is for sign (31 bits)

ii) 23 to 30 bit is for exponent

iii) 0-22 bit gives fraction (right most)

Next is to identify the elements

1st bit is sign bit

1 indicates negative and 0 indicates positive

Thus we can conclude, the given number is a positive number.