IEEE 754 Single Precision Floating Point System:

• Sep 23rd 2010, 10:20 AM
Celcius
IEEE 754 Single Precision Floating Point System:
Determine the smallest floating point number x greater than 1 that can be
represented exactly in a binary single precision floating point system.
Determine the quantity ε = x - 1 (This is called machine epsilon).

Info on floating point number system: Floating point - Wikipedia, the free encyclopedia
32 bits.
1 bit sign
8 bits for exponent
23 bits for significand

I'm thinking something like -

0|01111111|00000000000000000000001

Which equals 1.0000001
• Sep 23rd 2010, 10:29 PM
CaptainBlack
Quote:

Originally Posted by Celcius
Determine the smallest floating point number x greater than 1 that can be
represented exactly in a binary single precision floating point system.
Determine the quantity ε = x - 1 (This is called machine epsilon).

Info on floating point number system: Floating point - Wikipedia, the free encyclopedia
32 bits.
1 bit sign
8 bits for exponent
23 bits for significand

I'm thinking something like -

0|01111111|00000000000000000000001

Which equals 1.0000001

I would leave it as $1+2^{-23}$.

I would also in passing mention normalisation (the assumed most significant bit is 1 so it is not held in the mantissa).

CB
• Sep 26th 2010, 03:22 AM
HallsofIvy
Note that Captain Black's suggested answer is exact while yours is not!