Float representation using normalised mantissa

Question

while representing an exponent in floating point number why do we add a biased term? What is the benifit of adding this??

Comments

Answer 1

Actual Exponent can be -ve too. So to represent these in normal (2’s complement) format you would need a sign bit so that should be the MSB.
But again, the mantissa can be -ve, for that as well you would need a sign bit, so there must be MSB for that too.
By definition 2 MSBs are NOT possible, Hence some conversion is required.
[even if we try to work it out we would be wasting an extra bit, because using a bias can save us the storage of that extra so called MSB]

Why was the bias chosen as 127 for ieee 754  32-bit format ?
BIAS can be any arbitrary number but Using this bias will allow for a lexicographic arrangement so that BE = 01111111 (127) is AE = 0 and BE = 10000000 (128) is AE = 1
[unlike 2’s complement where 01111111 is 127 and 10000000 is -128]