UGC NET Questions (Paper – 1)

In 8-bit one’s complement, a leading 1 indicates a negative number. To find its magnitude, invert all bits and read the result as an unsigned binary number. Inverting 10011001₂ gives 01100110₂, which equals 64 + 32 + 4 + 2 = 102. Therefore, 10011001₂ represents −102 in one’s complement.

Option A:
Option A is correct because one’s complement encodes −X as the bitwise inversion of +X. Since 10011001₂ inverts to 01100110₂ (= 102), the represented value is −102.

Option B:
Option B (−104) would require the inverted magnitude to be 104 (01101000₂). But the inversion here is 01100110₂ (=102), so it cannot be −104.

Option C:
Option C (−127) is the most negative magnitude possible in 8-bit one’s complement and corresponds to inverting 01111111₂. The given pattern does not invert to 127, so this is incorrect.

Option D:
Option D (−128) is not representable in 8-bit one’s complement (the range is −127 to +127, with both +0 and −0). Hence −128 cannot be the answer.

Binary Coded Decimal encodes each decimal digit separately as a 4-bit binary value. This allows decimal digits 0 through 9 to be represented by binary patterns from 0000₂ to 1001₂. Using 4 bits per digit is sufficient and convenient for hardware that interfaces with decimal displays. Therefore, each BCD digit occupies 4 bits.

Option A:
Option A, 3 bits, can represent only 8 distinct values, which is insufficient for ten digits 0 through 9. Thus, 3 bits cannot encode all decimal digits in BCD.

Option B:
Option B, 2 bits, allows only 4 combinations and is even more inadequate. It cannot uniquely represent all decimal digits.

Option C:
Option C is correct because 4 bits give 16 combinations, enough for digits 0–9 and some unused patterns. This is the standard sizing for BCD fields.

Option D:
Option D, 8 bits, would be wasteful for representing a single decimal digit, since 8 bits can represent 256 different values. BCD typically keeps the encoding compact with 4 bits per digit.

To find the two's complement of −18 in 8 bits, we first write +18 as binary: 00010010₂. We then invert the bits to obtain the one's complement 11101101₂ and add 1 to get 11101110₂. This 8-bit pattern uniquely represents −18 in two's complement form. Hence, 11101110₂ is the correct encoding.

Option A:
Option A correctly follows the two's complement procedure: write the positive magnitude, invert all bits, and add one. The resulting pattern 11101110₂ yields −18 when interpreted as a signed 8-bit integer. Thus, this option matches both the algorithm and the value.

Option B:
Option B, 11101101₂, is only the one's complement of +18 and does not include the final +1 step. In two's complement arithmetic, stopping at the one's complement gives the wrong numeric value. Therefore, this pattern does not represent −18.

Option C:
Option C, 11110010₂, corresponds to a different negative number when decoded as two's complement (−14). It arises from using an incorrect starting magnitude or misapplying the inversion and addition process.

Option D:
Option D, 10010010₂, resembles the sign-magnitude representation of −18, with the sign bit set and remaining bits for magnitude. However, two's complement is not sign-magnitude, so this pattern is not correct in that coding system.