Created
January 10, 2018 22:42
-
-
Save hoehrmann/75c594500e293deb4dd1151a7b800e46 to your computer and use it in GitHub Desktop.
Binary boolean operation truth tables, various versions
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
0 !| < > & A B == | |
+---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ | |
| 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | |
+---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ | |
| 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | |
+---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ | |
+---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ | |
| 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | |
+---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ | |
| 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | 0 | 0 | | |
+---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ +---+---+ | |
1 | !< !> !& !A !B != | |
+---+---+ | |
!A | 1 | 1 | | |
+---+---+ | |
| 0 | 0 | | |
+-------+ | |
!|, nor A | | |
+---+---+ +---+---+ +---+---+ | |
!(A | B) | 1 | 0 | | 0 | 0 | | 0 | 1 | + | |
+---+---+ +---+---+ +---+---+ !(!A ^ !B) | |
| 0 | 0 | | 1 | 1 | | 1 | 1 | | |
+-------+ --------+ --------+ | |
< ==, <=> !<, >= | |
+---+---+ +---+---+ +---+---+ | |
!A & B | 0 | 1 | | 1 | 0 | | 1 | 0 | A | !B | |
+---+---+ +---+---+ +---+---+ | |
+---+---+ | 0 | 0 | | 0 | 1 | | 1 | 1 | +---+---+ | |
0 | 0 | 0 | +-------+ +-------+ +-------+ | 1 | 1 | 1 | |
+---+---+ > !=, ^, - !>, <= +---+---+ | |
| 0 | 0 | +---+---+ +---+---+ +---+---+ | 1 | 1 | | |
+---+---+ | 0 | 0 | | 0 | 1 | | 1 | 1 | +---+---+ | |
+---+---+ +---+---+ +---+---+ | |
A & !B | 1 | 0 | | 1 | 0 | | 0 | 1 | !A | B | |
+-------+ +-------+ +-------+ | |
& B !&, nand | |
+---+---+ +---+---+ +---+---+ | |
* | 0 | 0 | | 0 | 1 | | 1 | 1 | !(A & B) | |
!(!A v !B) +---+---+ +---+---+ +---+---+ | |
| 0 | 1 | | 0 | 1 | | 1 | 0 | | |
+-------+ --------+ +-------+ | |
+---+---+ | |
!B | 1 | 0 | | |
+---+---+ | |
| 1 | 0 | | |
+-------+ | |
!& s | |
!0 rst | |
!< rt | |
!= s | |
!> rt | |
!A t | |
!B t | |
!| st | |
&& st | |
0 st | |
< t | |
== rst | |
> t | |
A t | |
B t | |
|| s | |
+---B---+ | |
!A | 0 | 1 | | |
+----+---+---+ | |
| 0 | 1 | 1 | | |
A----+---+---+ | |
| 1 | 0 | 0 | | |
+------------+ | |
+---B---+ +---B---+ +---B---+ | |
!|| | 0 | 1 | A | 0 | 1 | || | 0 | 1 | | |
+----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 1 | 0 | | 0 | 0 | 0 | | 0 | 0 | 1 | | |
A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 0 | 0 | | 1 | 1 | 1 | | 1 | 1 | 1 | | |
+------------+ +------------+ +------------+ | |
+---B---+ +---B---+ +---B---+ | |
< | 0 | 1 | == | 0 | 1 | !< | 0 | 1 | | |
+----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 0 | 1 | | 0 | 1 | 0 | | 0 | 1 | 0 | | |
+---B---+ A----+---+---+ A----+---+---+ A----+---+---+ +---B---+ | |
0 | 0 | 1 | | 1 | 0 | 0 | | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 0 | 1 | | |
+----+---+---+ +------------+ +------------+ +------------+ +----+---+---+ | |
| 0 | 0 | 0 | | 0 | 1 | 1 | | |
A----+---+---+ +---B---+ +---B---+ +---B---+ A----+---+---+ | |
| 1 | 0 | 0 | > | 0 | 1 | != | 0 | 1 | !> | 0 | 1 | | 1 | 1 | 1 | | |
+------------+ +----+---+---+ +----+---+---+ +----+---+---+ +------------+ | |
| 0 | 0 | 0 | | 0 | 0 | 1 | | 0 | 1 | 1 | | |
A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 1 | 0 | | 1 | 1 | 0 | | 1 | 0 | 1 | | |
+------------+ +------------+ +------------+ | |
+---B---+ +---B---+ +---B---+ | |
&& | 0 | 1 | B | 0 | 1 | !&& | 0 | 1 | | |
+----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 0 | 0 | | 0 | 0 | 1 | | 0 | 1 | 1 | | |
A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 0 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | | |
+------------+ +------------+ +------------+ | |
+---B---+ | |
!B | 0 | 1 | | |
+----+---+---+ | |
| 0 | 1 | 0 | | |
A----+---+---+ | |
| 1 | 1 | 0 | | |
+------------+ | |
+---+---+ | |
!A | 1 | 1 |-r | |
+---+---+-s | |
| 0 | 0 |+t | |
+-------+ | |
!|, nor A | | |
+---+---+ +---+---+ +---+---+ | |
!(A | B) | 1 | 0 | | 0 | 0 |-r | 0 | 1 | + | |
+---+---+ +---+---+-s +---+---+ | |
| 0 | 0 | | 1 | 1 |+t | 1 | 1 | | |
+-------+ --------+ --------+ | |
< ==, <=> !<, >= | |
+---+---+ +---+---+ +---+---+ | |
!A & B | 0 | 1 | | 1 | 0 |+r | 1 | 0 | A | !B | |
+---+---+ +---+---++s +---+---+ | |
+---+---+ | 0 | 0 | | 0 | 1 |+t | 1 | 1 | +---+---+ | |
0 | 0 | 0 | +-------+ +-------+ +-------+ | 1 | 1 | 1 | |
+---+---+ > !=, ^, - !>, <= +---+---+ | |
| 0 | 0 | +---+---+ +---+---+ +---+---+ | 1 | 1 | | |
+---+---+ | 0 | 0 | | 0 | 1 |-r | 1 | 1 | +---+---+ | |
+---+---+ +---+---++s +---+---+ | |
A & !B | 1 | 0 | | 1 | 0 |-t | 0 | 1 | !A | B | |
+-------+ +-------+ +-------+ | |
& B !&, nand | |
+---+---+ +---+---+ +---+---+ | |
* | 0 | 0 | | 0 | 1 |-r | 1 | 1 | !(A & B) | |
+---+---+ +---+---+-s +---+---+ | |
| 0 | 1 | | 0 | 1 |+t | 1 | 0 | | |
+-------+ --------+ +-------+ | |
+---+---+ | |
!B | 1 | 0 | | |
+---+---+ | |
| 1 | 0 | | |
+-------+ | |
+---B---+ +---B---+ +---B---+ +---B---+ | |
0 | 0 | 1 | && | 0 | 1 | > | 0 | 1 | A | 0 | 1 | | |
+----+---+---+ +----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 0 | 0 | | 0 | 0 | 0 | | 0 | 0 | 0 | | 0 | 0 | 0 | | |
A----+---+---+ A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 0 | 0 | | 1 | 0 | 1 | | 1 | 1 | 0 | | 1 | 1 | 1 | | |
+------+---+-----+------+---+-----+------+---+-----+-------+---+----+ | |
| A && !A | A && B | A > B | A // B | | |
| | A * B | A >> B | A << B | | |
| | | A && !B | | | |
+----------------+----------------+----------------+----------------+ | |
+---B---+ +---B---+ +---B---+ +---B---+ | |
< | 0 | 1 | B | 0 | 1 | !== | 0 | 1 | || | 0 | 1 | | |
+----+---+---+ +----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 0 | 1 | | 0 | 0 | 1 | | 0 | 0 | 1 | | 0 | 0 | 1 | | |
A----+---+---+ A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 0 | 0 | | 1 | 0 | 1 | | 1 | 1 | 0 | | 1 | 1 | 1 | | |
+------+---+-----+------+---+-----+------+---+-----+-------+---+----+ | |
| A < B | | A !== B | A || B | | |
| !A & B | | A xor B | A + B | | |
| | | A - B | | | |
| | | A ^ B | | | |
+----------------+----------------+----------------+----------------+ | |
+---B---+ +---B---+ +---B---+ +---B---+ | |
!|| | 0 | 1 | == | 0 | 1 | !B | 0 | 1 | !< | 0 | 1 | | |
+----+---+---+ +----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 1 | 0 | | 0 | 1 | 0 | | 0 | 1 | 0 | | 0 | 1 | 0 | | |
A----+---+---+ A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 0 | 0 | | 1 | 0 | 1 | | 1 | 1 | 0 | | 1 | 1 | 1 | | |
+------+---+-----+------+---+-----+------+---+-----+-------+---+----+ | |
| A nor B | A == B | | A !< B | | |
| A !|| B | A <=> B | | A >= B | | |
| !A && !B | | | A || !B | | |
| | | | A ** B | | |
+----------------+----------------+----------------+----------------+ | |
+---B---+ +---B---+ +---B---+ +---B---+ | |
!A | 0 | 1 | !> | 0 | 1 | !&& | 0 | 1 | 1 | 0 | 1 | | |
+----+---+---+ +----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 1 | 1 | | 0 | 1 | 1 | | 0 | 1 | 1 | | 0 | 1 | 1 | | |
A----+---+---+ A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 0 | 0 | | 1 | 0 | 1 | | 1 | 1 | 0 | | 1 | 1 | 1 | | |
+------+---+-----+------+---+-----+------+---+-----+-------+---+----+ | |
| | A => B | A nand B | A || !A | | |
| | !A || B | | | | |
| | | | | | |
+----------------+----------------+----------------+----------------+ | |
----------------------------------------------------------------------- | |
- | |
----------------------------------------------------------------------- | |
+---+---+ | |
!A | 1 | 1 | | |
+---+---+ | |
| 0 | 0 | | |
+-------+ | |
!||, nor A ||, + | |
+---+---+ +---+---+ +---+---+ | |
!A && !B | 1 | 0 | | 0 | 0 | | 0 | 1 | | |
+---+---+ +---+---+ +---+---+ | |
| 0 | 0 | | 1 | 1 | | 1 | 1 | | |
+-------+ --------+ --------+ | |
< ==, <=> !<, >= | |
+---+---+ +---+---+ +---+---+ | |
!A & B | 0 | 1 | | 1 | 0 | | 1 | 0 | A || !B | |
+---+---+ +---+---+ +---+---+ | |
+---+---+ | 0 | 0 | | 0 | 1 | | 1 | 1 | +---+---+ | |
0 | 0 | 0 | +-------+ +-------+ +-------+ | 1 | 1 | 1 | |
+---+---+ > !=, ^, - !>, <= +---+---+ | |
| 0 | 0 | +---+---+ +---+---+ +---+---+ | 1 | 1 | | |
+---+---+ | 0 | 0 | | 0 | 1 | | 1 | 1 | +---+---+ | |
+---+---+ +---+---+ +---+---+ | |
A && !B | 1 | 0 | | 1 | 0 | | 0 | 1 | !A || B | |
+-------+ +-------+ +-------+ | |
& B !&&, nand | |
+---+---+ +---+---+ +---+---+ | |
* | 0 | 0 | | 0 | 1 | | 1 | 1 | | |
+---+---+ +---+---+ +---+---+ | |
| 0 | 1 | | 0 | 1 | | 1 | 0 | | |
+-------+ --------+ +-------+ | |
+---+---+ | |
!B | 1 | 0 | | |
+---+---+ | |
| 1 | 0 | | |
+-------+ | |
----------------------------------------------------------------------- | |
- | |
----------------------------------------------------------------------- | |
+---+---+ | |
!A | 1 | 1 | | |
+---+---+ | |
| 0 | 0 | | |
+-------+ | |
!||,nor A ||, + | |
+---+---+ +---+---+ +---+---+ | |
!A && !B | 1 | 0 | | 0 | 0 | | 0 | 1 | | |
+---+---+ +---+---+ +---+---+ | |
| 0 | 0 | | 1 | 1 | | 1 | 1 | | |
+-------+ --------+ --------+ | |
< ==, <=> !<, >= | |
+---+---+ +---+---+ +---+---+ | |
!A & B | 0 | 1 | | 1 | 0 | | 1 | 0 | A || !B | |
+---+---+ +---+---+ +---+---+ | |
+---+---+ | 0 | 0 | | 0 | 1 | | 1 | 1 | +---+---+ | |
0 | 0 | 0 | +-------+ +-------+ +-------+ | 1 | 1 | 1 | |
+---+---+ > !=,^,- !>, <= +---+---+ | |
| 0 | 0 | +---+---+ +---+---+ +---+---+ | 1 | 1 | | |
+---+---+ | 0 | 0 | | 0 | 1 | | 1 | 1 | +---+---+ | |
+---+---+ +---+---+ +---+---+ | |
A && !B | 1 | 0 | | 1 | 0 | | 0 | 1 | !A || B | |
+-------+ +-------+ +-------+ | |
&&, * B !&&, nand | |
+---+---+ +---+---+ +---+---+ | |
| 0 | 0 | | 0 | 1 | | 1 | 1 | | |
+---+---+ +---+---+ +---+---+ | |
| 0 | 1 | | 0 | 1 | | 1 | 0 | | |
+-------+ --------+ +-------+ | |
+---+---+ | |
!B | 1 | 0 | | |
+---+---+ | |
| 1 | 0 | | |
+-------+ | |
----------------------------------------------------------------------- | |
+---B---+ | |
!A | 0 | 1 | | |
+----+---+---+ | |
| 0 | 1 | 1 | | |
A----+---+---+ | |
| 1 | 0 | 0 | | |
+------------+ | |
+---B---+ +---B---+ +---B---+ | |
!|| | 0 | 1 | A | 0 | 1 | || | 0 | 1 | | |
+----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 1 | 0 | | 0 | 0 | 0 | | 0 | 0 | 1 | | |
A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 0 | 0 | | 1 | 1 | 1 | | 1 | 1 | 1 | | |
+------------+ +------------+ +------------+ | |
< == !< | |
+----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 0 | 1 | | 0 | 1 | 0 | | 0 | 1 | 0 | | |
+---B---+ A----+---+---+ A----+---+---+ A----+---+---+ +---B---+ | |
0 | 0 | 1 | | 1 | 0 | 0 | | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 0 | 1 | | |
+----+---+---+ +------------+ +------------+ +------------+ +----+---+---+ | |
| 0 | 0 | 0 | | 0 | 1 | 1 | | |
A----+---+---+ A----+---+---+ | |
| 1 | 0 | 0 | > != !> | 1 | 1 | 1 | | |
+------------+ +----+---+---+ +----+---+---+ +----+---+---+ +------------+ | |
| 0 | 0 | 0 | | 0 | 0 | 1 | | 0 | 1 | 1 | | |
A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 1 | 0 | | 1 | 1 | 0 | | 1 | 0 | 1 | | |
+------------+ +------------+ +------------+ | |
&& B !&& | |
+----+---+---+ +----+---+---+ +----+---+---+ | |
| 0 | 0 | 0 | | 0 | 0 | 1 | | 0 | 1 | 1 | | |
A----+---+---+ A----+---+---+ A----+---+---+ | |
| 1 | 0 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | | |
+------------+ +------------+ +------------+ | |
!B | |
+----+---+---+ | |
| 0 | 1 | 0 | | |
A----+---+---+ | |
| 1 | 1 | 0 | | |
+------------+ | |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment