Considering 2's complement representation for negative numbers, what is the…

In an n-bit two's complement representation, the most significant bit (MSB) carries a negative positional weight of -27 for 8 bits (in general -2(n-1)), while every other bit keeps its usual positive weight 2k. Adding up all the weighted bits directly gives the signed decimal value — no separate sign symbol is needed.

1. For an 8-bit register, the bit weights from the most significant bit (leftmost) to the least significant bit (rightmost) are -27, 26, 25, 24, 23, 22, 21, 20, i.e., -128, 64, 32, 16, 8, 4, 2, 1.

2. In the given pattern 10000000, only the most significant bit is 1; every other bit is 0.

3. Multiplying each bit by its weight and summing: (1 × -128) + (0 × 64) + (0 × 32) + (0 × 16) + (0 × 8) + (0 × 4) + (0 × 2) + (0 × 1) = -128.

Cross-check using the invert-and-add-one rule for negative numbers: inverting every bit of 10000000 gives 01111111 (= 127 in unsigned binary); adding 1 gives 10000000 (= 128 in unsigned binary). Since the sign bit is 1, the decimal value is -128 — the same result as the direct weighted-sum method.