The float using 7 bit exponent and 16 bit signficand for 277.431 was shown to be : 0 1000111 0001010101101110 Converting back : Bias Use formula 2^(n-1) - 1 where n is the size of the exponent. 2^(7-1)-1 = 63 bias Exponent 10000111 1 0 0 0 1 1 1 1 2 4 8 17 35 71 71 - 63 (bias) = 8 Signifcand 0001010101101110 Remember to put the invisible 1. back on : (b at the end of the string of 0s and 1s means binary) 1.0001010101101110b * 2^8 100010101.01101110b 1 0 0 0 1 0 1 0 1 1 2 4 8 17 34 69 138 277 .01101110 . 0 .5 1 .25 .25 1 .125 .125 0 .0625 1 .03125 .03125 1 .015625 .015625 1 .0078125 .0078125 0 .00390625 .4296375 Original 277.431