Autosave: 2024-03-19 07:30:04

zk/Twos_complement.md

@@ -12,8 +12,32 @@ created: Tuesday, March 19, 2024
 - _Two's complement_ is a method for representing signed numbers (negative
   integers) in binary.
 
+- The two's complement of a given binary integer is its negative equivalent.
+
 ## Detail
 
+### Procedural steps
+
+Two's complement divides the available word length (see
+[[Binary_encoding|binary encoding]]) into two subsets: one for negative integrs
+and one for positive integers.
+
+Take the binary encoding of decimal five (`0101`). Its complement is `1011`.
+
+The procedure for deriving the complement is as follows.
+
+To derive the complement of an unsigned number:
+
+1. Take the unsigned number and invert its digits: `0` becomes `1`, `1` becomes
+   `0`
+2. Add one
+
+![](/img/unsigned-to-signed.png)
+
+To derive the unsigned equivalent of a signed number
+
+### Formal expression
+
 ## Applications
 
 ## Related notes