UGC NET Questions (Paper – 1)

The decimal number 255 is one less than 256, which is 16². In hexadecimal, 16² corresponds to 100₁₆, so 255 must be written as 1 less than that, which is FF₁₆. Each F represents 15, and 15×16 + 15 = 240 + 15 = 255. Thus, FF₁₆ is the correct hex representation of 255₁₀.

Option A:
Option A correctly uses the relationship between powers of 16 and the decimal system. It recognises that FF₁₆ is the maximum value in two hex digits, analogous to 255 in decimal. This makes it a standard boundary value in byte-oriented systems.

Option B:
Option B, F0₁₆, equals 15×16 + 0 = 240 in decimal, which is smaller than 255. It neglects the contribution of the least significant digit required to reach 255. Hence it is an underestimation.

Option C:
Option C, FE₁₆, represents 15×16 + 14 = 254 in decimal, which is close but still one less than the required value. This corresponds to 254₁₀, not 255₁₀.

Option D:
Option D, F1₁₆, corresponds to 15×16 + 1 = 241 in decimal, which again does not equal 255. Since only FF₁₆ gives 255, this option cannot be correct.

The 8-bit pattern 11111111₂ can be grouped into two nibbles: 1111₂ and 1111₂. Each nibble corresponds to the hex digit F (decimal 15). Combining them gives FF₁₆. Therefore, 11111111₂ maps to FF₁₆.

Option A:
Option A correctly uses nibble-to-hex mapping: 1111₂ = F, so 11111111₂ = FF₁₆.

Option B:
Option B, FE₁₆, would correspond to 11111110₂ and thus to decimal 254, one less than the maximum.

Option C:
Option C, F0₁₆, corresponds to 11110000₂, which is decimal 240 and not the full 8-bit maximum.

Option D:
Option D, 0F₁₆, corresponds to 00001111₂, a value much smaller than 11111111₂.