All courses › Embedded Systems and Instrumentation › Two's Complement

Two's Complement

Two's complement is the standard way computers represent negative integers in a fixed number of bits. The top bit signals the sign, and a negative number $-x$ is represented as the unsigned bit pattern of $2^n-x$ . This makes addition work the same way for positive and negative numbers, with no special cases.

-x \to 2^n-x

bit pattern for a negative number in n-bit two's complement

[-2^{n-1},\ 2^{n-1}-1]

range of an n-bit signed integer

Symbols

$n$	number of bits
$x$	the number's absolute value

Example

$-5$ as 8-bit two's complement:

$2^8-5=251=\texttt{0xFB}$ .

Remember to subtract from

2^n

, not just flip the sign bit – that gives the wrong answer.

Practise number systems and digital logic for free →

← Number Systems · Logic Gates →

Part of Embedded Systems and Instrumentation: Number systems and digital logic.