Decimal value of 111.011₂ – UGC NET Question

To convert 111.011₂ to decimal, we sum the weighted values of each bit. The integer part 111₂ equals 4 + 2 + 1 = 7. The fractional part .011₂ equals 0/2 + 1/4 + 1/8 = 0.375. Adding 7 and 0.375 gives 7.375. Therefore, the correct decimal equivalent is 7.375.

Option A:
If we interpreted the value as 7.25, the fractional part would need to be .01₂, which equals 0.25. However, 111.011₂ contains two fractional ones at positions 1/4 and 1/8, so the fraction is 0.375, not 0.25. Thus this option is not correct.

Option B:
7.375 matches the sum of 7 from the integer part and 0.375 from the fractional part .011₂. Each bit contributes correctly according to its negative power of two. This makes 7.375 the correct conversion from binary to decimal.

Option C:
A value of 7.5 would require the fractional part to be .1₂, corresponding to 0.5. Since the given binary fraction has bits in the 1/4 and 1/8 places instead, the value does not reach 7.5. Hence this option is incorrect.

Option D:
7.625 would correspond to .101₂ as the fractional portion, giving 0.625. The actual fraction .011₂ is 0.375, so 7.625 does not match the given binary fraction either.