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supposed to be in binary, the answer is 31, because if you have 3 bits as the ex

ID: 3909959 • Letter: S

Question

supposed to be in binary, the answer is 31, because if you have 3 bits as the exponent then it would be 4 - 0, giving you 2^4 and then multiply 1.1111 by that, giving 31

In IEEE single precision floating point, which is greater: (circle one)

i.   The number of representable numbers between 1 and 2 inclusive. ii.   The number of representable numbers between 2 and 3 inclusive. iii. They are the same.

COULD SOMEONE EXPLAIN WHY THEY ARE THE SAME? I have seen that this is the answer multiple people have chosen - I don't understand what "1 and 2 and 2 and 3 inclusive" are...

Explanation / Answer

If the numbers are represented in 32 bit format they will be same because we can specify

The exponent and sign bit in 1 way only and the number of representable numbers depend on the number of mantissa bits which is same for both. Hence the answer is they will be same