Consider a 16-bit Floating-Point format following IEEE Std 754 with one signed bit, 4-bit exponent and 11-bit fraction. x = ( − 1 ) S × ( 1 + F r a c t i o n ) × 2 ( E x p o n e n t − B i a s ) x = (-1)^S \times (1+Fraction) \times 2^{(Exponent-Bias)} x = ( − 1 ) S × ( 1 + F r a c t i o n ) × 2 ( E x p o n e n t − B ia s )
A (a) The maximum positive FP number in this format is 1.1111 1111 111 × 2 7 1.1111\,1111\,111 \times 2^7 1.1111 1111 111 × 2 7 B (b) The smallest positive de-normalized number is 1.0 × 2 − 17 1.0 \times 2^{-17} 1.0 × 2 − 17 C (c) To ensure exponent is unsigned, the bias should be 15.
D (d) Floating-point addition requires aligning the binary points by shifting the operand with the smaller exponent; otherwise, shifting the operand with the larger exponent could make its fraction excessively large and result in overflow, while excessive shifting of the smaller exponent operand may cause its fraction to be truncated.
