Consider a 8-bit floating-point representation based on the IEEE floating-point

Question

Consider a 8-bit floating-point representation based on the IEEE floating-point format, with one sign bit, 4 exponent bits and 3 fraction bits. The exponent bias follows the IEEE standarod. Interpret the bitstring 0_0111 0012 using this 8-bit floating-point representation and fill in the table below. You may use expressions if it's useful. Field Mean The value represented by considering the exponent field to be an unsigned integer (as a decimal value) The value of the exponent after biasing (as a decimal value The numeric weight of the exponent (as a decimal value) The value of the fraction (as a fraction such as 3/4 or the exact floating point number) The value of the significand (as a fraction such such as 7/4 or the exact floating point number) The value of the number in decimal. The 's' is equal to +1 if the number is positive and -1 if it is negative Value 2E

Explanation / Answer

To interpret a 8-bit number, first separate out the sign-bit, exponent and fractional parts.

Now, you have the number in the form: b0 b1b2b3b4 b5b6b7.

The number in decimal form is just : -1b0 x 2((b1b2b3b4)10 - 7) x (1.b5b6b7)2

Field Value e 7 E 0 2E 1 f 0.125 M 1.125 s*2E*M 1.125

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