Question

Given the following representation of a floating number, what is the equivalent decimal number considering 7bits for exponent and 16bits for mantissa?

0 | 1000111 | 1100110010000000

Answer 1

i'm guessing the first bit is the sign, do you know what the exponent bias is?

i'm going to assume the exponent bias is 64

Exponent:
1000111 = 1 + 1*2 + 1*2^2 + 0*2^3 + 0*2^4 + 0*2^5 + 1*2^6
1000111 = 1 + 2 + 4 + 0 + 0 + 0 + 64
1000111 = 71

and with a bias of 64 the exponent is 71 - 64 = 7

Mantissa:
1100110010000000 = 52352 (i cheated =P but hopefully you can work it out =))

so you should get 52352 * 2^7 = 6701056

hope this helps