Question

When using 14-bit floating point excess 16 biased exponent, the fields will be used as

Select one:

a. 1 sign bit, a 6-bit exponent field and a 7-bit significand field

b. 1 sign bit, a 7-bit exponent field and a 6-bit significand field

c. 1 sign bit, a 4-bit exponent field and a 9-bit significand field

d. 1 sign bit, a 5-bit exponent field and an 8-bit significand field

Answer 1

The answer is option D.) 1 sign bit, a 5-bit exponent field and 8-bit significant field.

Explanation:

The representation of the floating point number is

sign(S)

exponent(E)

mantissa(M)

Sign field contains 1 bit.

If biased exponent field contains k bits the bias = 2^k-1 .

And we have given with the biased exponent i.e, excess-16.

Therefore Bias = 2^k-1 = 16 2^k-1 = 2⁴ , therefore k-1 = 4 k=5bits.

Therefore exponent field contains 5 bits.

Total number of bits = sign bit + exponent bits + mantissa bits.

14 bits = 1 + 5 + mantissa mantissa = 14 - 6 = 8 bits.

Therefore mantissa = 8 bits.

sign - 1 bits, exponent - 5 bits, mantissa - 8 bits.