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.

In two's complement, -1 is obtained by inverting all bits of +1 and then adding 1. For 8 bits, +1 is 00000001. Inverting gives 11111110, and adding 1 yields 11111111. Thus, the pattern 11111111 represents -1 in any fixed-width two's complement system, including 8 bits.

Option A:
Option A, 00000001, is the representation of +1, not -1. In unsigned binary and two's complement, this pattern always denotes a positive value. Therefore, it cannot be used for -1 in 8-bit two's complement.

Option B:
Option B, 10000000, represents the most negative value in 8-bit two's complement. Specifically, it corresponds to -128, derived from -2^(n-1). Because -128 is far from -1, this pattern is not correct for the given decimal number.

Option C:
Option C, 01111111, corresponds to the largest positive value, which is +127 in 8-bit two's complement. All leading bits except the sign bit are 1, making it a high positive integer. Thus, it cannot represent -1.

Option D:
Option D, 11111111, results directly from taking the two's complement of 00000001. It encodes -1 consistently in 8-bit signed arithmetic. This is why all bits set to 1 in two's complement signify -1, making this option correct.

For an 8-bit two's complement number starting with 1, we know it is negative. To find its decimal value, we invert the bits and add 1. The inversion of 11001011₂ is 00110100₂, and adding 1 gives 00110101₂, which is 53 in decimal. Therefore, the original 11001011₂ represents −53.

Option A:
Option A correctly performs the two-step process of inversion and addition to decode the negative value. It recognises that the pattern encodes a negative number and finds its magnitude as 53, then assigns the negative sign. Thus, −53 is the correct interpretation.

Option B:
Option B, −75, would require the magnitude bits after inversion and increment to equal 75, which they do not. This choice indicates a miscalculation in either the inversion step or the final addition.

Option C:
Option C, −77, similarly suggests a different magnitude than the one actually encoded by the bit pattern. Since decoding yields 53, this option does not match the numeric content of the 8-bit sequence.

Option D:
Option D, −69, also conflicts with the calculated magnitude. It represents another negative value that is not supported by the structure of 11001011₂. Hence, it is incorrect.