UGC NET Questions (Paper – 1)

In BCD, each group of four bits represents one decimal digit independently. The pattern 0100 corresponds to the digit 4, and 1001 corresponds to the digit 9. Placing these digits side by side yields the decimal number 49. Therefore, 0100 1001 in BCD is decoded as 49₁₀.

Option A:
Option A correctly interprets each 4-bit group as a separate digit, reflecting the nature of BCD as a digit-wise encoding. It recognises 0100 as 4 and 1001 as 9, leading to the decimal numeral 49. Thus, this option is consistent with BCD rules.

Option B:
Option B, 41, would arise if the second nibble 1001 were incorrectly decoded as 1 instead of 9, which conflicts with the standard binary mapping. Since 0001 represents 1 and not 1001, this interpretation is mistaken.

Option C:
Option C, 94, reverses the digit order, as if the first nibble were read as 9 and the second as 4. However, 0100 is definitively 4 and 1001 is 9, so reversing them does not follow the given bit sequence.

Option D:
Option D, 59, assigns 0100→5 and 1001→9 or introduces some other mapping error. The BCD code is fixed, and 0101 would be needed for the digit 5, not 0100. Hence this choice does not match the actual bit pattern.

The hexadecimal system has base 16, and 16 equals 2⁴. This means each hex digit corresponds exactly to a group of four bits. This makes hexadecimal a convenient shorthand for binary because each nibble maps to one hex digit.

Option A:
Option A correctly uses the identity 16 = 2⁴ to justify the four-bit groupings. It explains why 4-bit nibbles are natural units when representing binary values in hexadecimal form.

Option B:
Option B, 3, is associated with the octal system, where 8 = 2³ and each digit maps to three bits. It does not apply to base 16.

Option C:
Option C, 2, would yield only four combinations, insufficient to represent 16 different hex symbols (0–9 and A–F).

Option D:
Option D, 8, overestimates the bits per hex digit and would allow 256 combinations, which is far beyond the 16 needed.