## Two's complement representation of negative numbers

I will explain the two's complement expression for expressing negative numbers.

This is explained using the example of int8_t, which is an 8-bit signed integer type.

In computer architecture, there are several ways to represent negative numbers. Two's complement representation is one of them.

Let's write out the two's complement expression concretely.

Negative number | Negative number bit representation | Positive number (including 0) | Positive number bit representation < / td> |

-1 | 11111111 | 0 | 00000000 |

-2 | 11111110 | 1 | 00000001 |

-3 | 11111101 | 2 | 00000010 |

... | ... | ... | ... |

-126 | 10000010 | 125 | 01111101 |

-127 | 10000001 | 126 | 01111110 |

-128 | 10000000 | 127 | 01111111 |

Let's take a look at the characteristics of 2's complement representation.

- A positive number if the most significant bit is 0. Negative number if the most significant bit is 1
- 127 (maximum positive value) is 01111111
- -1 is 11111111
- -128 is 10000000
- Inverting the bits and summing them gives -1 (11111111)

The definition of 2's complement can be found everywhere, so please check it out (laughs).

### Can we assume that negative numbers are two's complement representations?

The C language specification does not define a negative number as a two's complement, but in many implementations, the representation of a negative number is much more two's complement than any other representation. think.

If you get a negative minimum when you add 1 to the positive maximum, you can be confident that your implementation is using 2's complement representation for negative numbers.

If the Numerical Library requires the implementation to have a two's complement as a negative representation, it can be checked with a simple calculation.

### What are the characteristics of 2's complement?

The feature of 2's complement is that subtraction can be expressed by addition.

2-3 = -1

This is the same as below.

# 00000010 + 11111101 = 11111111 2 + (-3) = -1

### Where is the nuance of 2's complement 2?

The naming method may have been wrong ...

I think forcibly.

Let's call the first discovered complement the one's complement. The sign changes by mere bit inversion.

Let's call the second found complement the two's complement. If you add 1 to the simple bit inversion, the sign will change.