Another method of representing signed numbers is two's complement. Most computers use this method to represent negative numbers. This method can be more effective when performing mathematical operations like adding and subtracting.
With two's complement, the bit at the far left of the bit pattern - the most significant bit or MSB - is used to indicate positive or negative and the remaining bits are used to store the actual size of the number. Positive numbers always start with a 0.
Four-bit, positive, two's complement numbers would be 0000 = 0, 0001 = 1, up to 0111 = 7. The smallest positive number is the smallest binary value.
Negative numbers always start with a 1. The smallest negative number is the largest binary value. 1111 is -1, 1110 is -2, 1101 is -3, etc down to 1000 which represents -8.
Find -1 using two's complement numbers
Find -4 using two's complement numbers
This table shows the two's complement set for 4-bit numbers.