Question

A floating-point representation with the following:

Exponent = 4 bits

Fraction = 4 bits

Sign bit = 1 bit

Bias = 7

What is the largest normalized number that could be represented in this format. Write the exact number in decimal, not an approximation.

Answer 1

The largest binary number is given as:

0 1111 1111

Sign bit = 0 (since the number is positive)

Exponent = 1111 - 0111 (bias) = 1000 = 8₁₀

Mantissa = 0.1111

After denormalizing the number, we get

1.1111 * 2⁸ = 1.9375 * 256 = 496