Suggest edit — two's complement

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---
title: "two's complement"
type: concept
related: [Inverses]
source: https://www.jemoka.com/posts/kbhtwo_s_complement/
confidence: high
status: active
---

Say we want to find the number which is the additive inverse (&ldquo;negative&rdquo;) of a number.
We can just flip each of the digit, and then add 1:
take \(0101\), invert it to get \(1010\) adding these two numbers will give you \(1111\). If we just added one more \(0001\), it will flip over to be \(0000\). Therefore, \(1010+0001 = 1011\) is the additive inverse of \(0101\). The left most bit being one: still a mark of whether or not something is negative. It just works backwards:
pros and cons of twos complement con: more difficult to represent and difficult to convert pro: only 1 representation for 0 pro: the most significant bit still indicates the sign of a number pro: addition works for any combination of positive/negative tricks all zeros: its always 0 zero plus all ones (011111&hellip;111): it always is the largest signed value and some middle value for unsigned all ones: its always -1 (11111 =&gt; 00000 +1 =&gt; 1) for signed one plus all zeros mnemonic for remembering where overflows happened Unsigned Signed