Chapter 3: Logic Gates
The Inverter:
The inverter changes one logic level to the opposite level.
Inverter Symbol
A
Inverter Truth Table
Input
Output
0
1
1
0
X
Logic Expression for the Inverter (or NOT gate):
𝑋 = 𝐴̅
The AND Gate:
The AND gate performs logical multiplication. In other words, in
order for the output of an AND gate to be a 1, both of the inputs must be 1 (or “HIGH”.)
AND Symbol
AND Truth Table
Input
A
B
X
0
0
0
0
1
0
1
0
0
1
1
1
Logic Expression for the AND gate:
𝑋 =𝐴∙𝐵
𝑜𝑟
Output
𝑋 = 𝐴𝐵
The OR Gate:
The OR gate performs logical addition. In other words, in order for the
output of an AND gate to be a 1, at least one of the inputs must be 1 (or “HIGH”.)
OR Symbol
OR Truth Table
Input
Output
A
B
X
0
0
0
0
1
1
1
0
1
1
1
1
Logic Expression for the OR gate:
𝑋 =𝐴+𝐵
The NAND Gate:
The NAND gate means “NOT-AND” and performs the opposite
function of an AND gate. In other words, the output of the NAND gate is high (or “1”)
only when both inputs are not high. The NAND gate is also called a universal gate
because it can be used to perform the function of any other gate.
NAND Symbol
NAND Truth Table
Input
A
B
A
B
X
0
0
1
0
1
1
1
0
1
1
1
0
Logic Expression for the NAND gate:
𝑋 =𝐴∙𝐵
𝑜𝑟
Output
𝑋 = 𝐴𝐵
The NOR Gate:
The NOR gate means “NOT-OR” and performs the opposite function
of an OR gate. In other words, the output of the NOR gate is high (or “1”) only when
neither inputs are high. The NOR gate is also called a universal gate because it can be
used to perform the function of any other gate.
NOR Symbol
NOR Truth Table
Input
A
B
Output
A
B
X
0
0
1
0
1
0
1
0
0
1
1
0
Logic Expression for the NOR gate:
𝑋 =𝐴+𝐵
The XOR Gate:
The XOR gate output is HIGH only when the two inputs are at
opposite logic levels.
XOR Symbol
XOR Truth Table
Input
A
B
X
Output
A
B
X
0
0
0
0
1
1
1
0
1
1
1
0
Logic Expression for the XOR gate:
𝑋 =𝐴⊕𝐵
The XNOR Gate:
The XNOR gate output is HIGH only when the two inputs are at the
same logic level.
XNOR Symbol
XNOR Truth Table
Input
A
B
Output
A
B
X
0
0
1
0
1
0
1
0
0
1
1
1
Logic Expression for the AND gate:
𝑋 =𝐴⊕𝐵