What would machine epsilon be for the storage scheme in prob

What would machine epsilon be for the storage scheme in problem above? How many digits of precision (base 10) would you expect for the number given above? What number would be represented if the number given above were a 32-bit integer?

Solution

Ans: unsigned integer

binary number: 10000011111010110000000000000000

decimal convertion:

1*2^31+1*2^25+1*2^24+1*2^23+1*2^22+1*2^21+1*2^19+1*2^17+1*2^16 = 2213216256

Most accurate representation of unsigned integer= 2213216256

or

signed integer:

binary number: 1 0000011111010110000000000000000

decimal conversion:

here first bit of left represents sign s=1 negative number

0000011111010110000000000000000

1*2^25+1*2^24+1*2^23+1*2^22+1*2^21+1*2^19+1*2^17+1*2^16 = -2081751040

Most accurate representation = -2081751040