Question

What's the decimal value of the following 8 bit floating point number? Suppose k=4 exponent bits, n=3 fraction bits, and the bias is 7

00111001

Answer 1

Answer: 1.125

Explanation:

k=4; exponent bits,

n=3; fraction bits

Given number is 0 0111 001

Exponent is 0111₂ = 7₁₀

Decimal Equivalent is 1.fff * 2^{exponent-bias}

Positive since the sign bit is 0

The number is 1.001 * 2^7-7 = 1.001

1.125₁₀

Answer 2

The given floating-point number is in the following format:

yamlCopy code0 0111 0010

Here, the sign bit is 0 which represents a positive number. The exponent bits are 0111 which represent the decimal value 7. The fraction bits are 001 which represent the binary fraction 0.001.

To calculate the decimal value, we use the following formula:

scssCopy code(-1)^s * (1 + f) * 2^(e-b)

where s is the sign bit, f is the fraction bits, e is the exponent bits, and b is the bias.

Substituting the values, we get:

scssCopy code(-1)^0 * (1 + 0.001) * 2^(7-7)
= 1.001 * 1= 1.001

Therefore, the decimal value of the given floating-point number is 1.001.