Two's Complement (CIE IGCSE Computer Science)

• Two's complement is a method of representing signed integers in binary form, where the leftmost bit represents the sign (0 for positive and 1 for negative)
• To convert a positive number to a two's complement 8-bit integer, first represent the number in binary form with leading zeros until it is 8 bits long. If the number is positive, the leftmost bit should be 0
• To convert a negative number to a two's complement 8-bit integer, first invert all the bits in the binary representation of the positive equivalent of the number (i.e., flip all the 1's to 0's and all the 0's to 1's). Then, add 1 to the result to obtain the two's complement representation

Two's complement walkthrough:

• The binary number 00101011 represents the positive integer 43 in 8-bit binary form
• E.g. to represent the negative integer -43 in two's complement 8-bit form, start by representing the positive equivalent of 43 in binary form: 00101011. Then invert all the bits to get 11010100, and add 1 to get 11010101