What is 37 on floating point notation?

Answer 1

G'day,

It depends upon your word size and notations use.

Irrespective of that, a floating point notation has three parts:

Sign Bit | Exponent | Mantissa

Sign Bit is always just one bit.

Size of Exponent depends upon a particular selection for a notation. Also, the encoding of Exponent could be in different notation, such as 2's comp, biased, excess, etc.

Similarly size of Mantissa depends upon the notation.

Here, for your question, I will take 32-bit word for FP and use the following convention.

Sign Bit | Exponent | Mantissa

1 | 8 bits | 23 bits

37 in 2's comp is 100101

This could be written as 100101.0000____

In normalised form, we start populating the Mantissa using first 1 from the left

Mantissa: 1001 0100 0000 0000 0000 000

If the radix point were at the extreme left of Mantissa, if would have to be moved 6 places to the right to get the original number. So we encode 6 in excess notation using 8 bits. This forms our Exponent.

Exponent: 1000 0110

Finally, the number is positive, hence the sign bit will be 0, interpreted as per 2's comp

Sign Bit: 0

Put this all together.

0 1000 0110 1001 0100 0000 0000 0000 00

is 37 in floating point.

This is correct to the best of my knowledge. If, however, someone has some correction, please do.

Cheers,

A