Editing Two's complement (section)

== Procedure ==
The following is the procedure for obtaining the two's complement representation of a given ''negative'' number in binary digits:

* Step 1: starting with the absolute binary representation of the number, with the leading bit being a sign bit;<ref>{{cite web|url=https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/DM3_TwosComplement_BP_9_22_14.pdf|title=Two's Complement|website=University of Rochester Academic Success Center}}</ref>
* Step 2: inverting (or flipping) all bits – changing every 0 to 1, and every 1 to 0;
* Step 3: adding 1 to the entire inverted number, ignoring any [[Integer overflow|overflow]]. Accounting for overflow will produce the wrong value for the result.

For example, to calculate the [[decimal]] number '''−6''' in binary from the number '''6''':

* Step 1: ''+6'' in decimal is ''0110'' in binary; the leftmost significant bit (the first 0) is the [[Sign (mathematics)|sign]] (just 110 in binary would be −2 in decimal). 
* Step 2: flip all bits in ''0110'', giving ''1001''. 
* Step 3: add the place value 1 to the flipped number ''1001'', giving ''1010''.

To verify that ''1010'' indeed has a value of ''−6'', add the place values together, but ''subtract'' the sign value from the final calculation. Because the most significant value is the sign value, it must be subtracted to produce the correct result: '''1010''' = '''−'''('''1'''×2<sup>3</sup>) + ('''0'''×2<sup>2</sup>) + ('''1'''×2<sup>1</sup>) + ('''0'''×2<sup>0</sup>) = '''1'''×−8 + '''0''' + '''1'''×2 + '''0''' = −6. 
{| class="wikitable"
|Bits:
|1
|0
|1
|0
|-
|Decimal bit value:
| '''−'''8
|4
|2
|1
|-
|Binary calculation:
|'''−'''('''1'''×2<sup>3</sup>)
|('''0'''×2<sup>2</sup>)
|('''1'''×2<sup>1</sup>)
|('''0'''×2<sup>0</sup>)
|-
|Decimal calculation:
|'''−'''('''1'''×8)
|'''0'''
|'''1'''×2
|'''0'''
|}

Note that steps 2 and 3 together are a valid method to compute the [[additive inverse]] <math>-n</math> of any (positive or negative) integer <math>n</math> where both input and output are in two's complement format. An alternative to compute <math>-n</math> is to use subtraction <math>0-n</math>. See below for subtraction of integers in two's complement format.