Question

What decimal number is represented by the binary 2’s complement 8-bit number 11100111? Show your work

Answer 1

In a signed binary two's complement, the first bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.
1110 0111 is the binary representation of a negative integer, on 8 bits.

* Run this step only if the number is negative *
Subtract 1 from the binary initial number:
1110 0111 - 1 = 1110 0110

* Run this step only if the number is negative *
Flip all the bits in the signed binary one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
!(1110 0110) = 0001 1001

0001 1001₍₂₎ =
(0 × 27 + 0 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20)₍₁₀₎ =
(0 + 0 + 0 + 16 + 8 + 0 + 0 + 1)₍₁₀₎ =
(16 + 8 + 1)₍₁₀₎ =
25₍₁₀₎

If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1110 0111₍₂₎ = -25₍₁₀₎

Number 1110 0111₍₂₎ converted from signed binary two's complement representation to an integer in the decimal system (in base 10):

1110 0111₍₂₎ = -25₍₁₀₎