Below you will find the 7 Logic Gates. These are fundamentals of electronics and are common knowledge to a good electronic engineer.
I have included their short hand name, as well as what they mean (i.e. XOR is short for Exclusive OR). A written description, truth table and 8-bit example should help you to understand them. Under each Logic Gate Symbol there is the equivalent ONLY using NAND gates. So all you need is a few '7400 Quad 2-input NAND Gates' to reproduce any one of these Logic Gates.
» NOT
Not
NOT NOT Using only NAND gates
Boolean Expression:




A
Description:
Output is true only when input is false, and vice versa. Commonly referred to as an inverter.
Truth Table:
Input Output
A A NOT B
0 1
1 0
8-bit example:
A 1001 0001
O 0110 1110

 
» AND
And
AND AND Using only NAND gates
Boolean Expression:




A · B
Description:
Output is true only when both inputs are true.
Truth Table:
Input Output
A B A AND B
0 0 0
0 1 0
1 0 0
1 1 1
8-bit example:
A 1001 1001
B 0000 1111
O 0000 1001

 
» NAND
Not And
NAND NAND Using only NAND gates
Boolean Expression:




A · B
Description:
Output is true only when either or both inputs are false.
Truth Table:
Input Output
A B A NAND B
0 0 1
0 1 1
1 0 1
1 1 0
8-bit example:
A 1001 1001
B 0000 1111
O 1111 0110

 
» OR
Inclusive Or
OR OR Using only NAND gates
Boolean Expression:




A + B
Description:
Output is true only when either or both inputs are true.
Truth Table:
Input Output
A B A OR B
0 0 0
0 1 1
1 0 1
1 1 1
8-bit example:
A 1001 1001
B 0000 1111
O 1001 1111

 
» NOR
Not Inclusive Or
NOR NOR Using only NAND gates
Boolean Expression:




A + B
Description:
Output is true only when both inputs are false.
Truth Table:
Input Output
A B A NOR B
0 0 1
0 1 0
1 0 0
1 1 0
8-bit example:
A 1001 1001
B 0000 1111
O 0110 0000

 
» XOR
Exclusive Or
XOR XOR Using only NAND gates
Boolean Expression:




A Θ B
Description:
Output is true only when one of the inputs are true.
Truth Table:
Input Output
A B A XOR B
0 0 0
0 1 1
1 0 1
1 1 0
8-bit example:
A 1001 1001
B 0000 1111
O 1001 0110

 
» XNOR
Exclusive Not Or
XNOR
XNOR Using only NAND gates
Boolean Expression:




A Θ B
Description:
Output is true only when both of the inputs are either true or flase.
Truth Table:
Input Output
A B A XNOR B
0 0 1
0 1 0
1 0 0
1 1 1
8-bit example:
A 1001 1001
B 0000 1111
O 0110 1001
       
 
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