The smallest integer that can be represented by an 8-bit number in 2's complement form is A. -256 B. -128 C. -127 D. 0

GATE 2013 · Digital Logic · Number Representation · easy

Answer: The smallest integer representable in 8-bit 2's complement is -128. Answer: B.

1. Apply 2's complement range formula: For n = 8 bits: Minimum value = -2^(8-1) = -2^7 = -128. The bit pattern is 10000000 (MSB=1, all others=0).
2. Verify bit pattern 10000000: 10000000: Value = -1*128 + 0*64 + 0*32 + 0*16 + 0*8 + 0*4 + 0*2 + 0*1 = -128 + 0 = -128. This is the smallest (most negative) representable value.