The two's complement is a way to represent negative numbers in binary when the minus sign is not available. The minus sign is substituted in the two's complement representation by a digit, usually the leading one.

• If the leading digit is 0, the number is positive.
• If the leading digit is 1, the number is negative.

To calculate the two's complement of a number:

1. If the number is negative, subtract it from the power of 2 with exponent corresponding to the number of bits of your chosen representation.
2. Convert the number to binary.
3. If the number was negative, add 1 to the proper position and pad with 0.
4. If the number was positive, left-pad the result with 0 to the desired length.

The 8-bit two's complement representation of −37 is 110110112. To find this result:

1. Subtract 37 from 2⁷: 128 − 37 =91.
2. Find the binary representation of 91:
   91 = 64 + 16 + 8 + 2 + 1
   = 1·2⁶ + 0·2⁵ + 1·2⁴ + 1·2³ + 0·2² + 1·2¹ + 1·2⁰
   =1011011
3. Place 1 in the correct position to mark that we started from a negative number:
   −3710 = 110110112