AND vs NAND vs OR vs NOR Logic Gates: Truth Tables and Symbols

This page compares AND, NAND, OR, and NOR gates, covering their truth tables and logic symbols. Digital logic circuits are largely built using basic logic gates like AND and OR. NAND and NOR gates are derived from AND and OR gates, respectively.

• The inputs (input-1, input-2) can be considered as logical values (True or False).
• We can also think of the inputs as voltage (True) or Ground (False).
• The output of the gate will also be voltage (true) or ground (false).

AND Logic Gate

Figure 1: AND gate logic symbol

The AND gate is an electronic circuit that outputs true (1) only if all its inputs are true. A dot (•) is used to represent the AND operation (A•B).

Figure 1 shows the AND logic gate symbol, and Table 1 presents the truth table:

Table 1: AND gate truth table

NAND Logic Gate

Figure 2: NAND gate logic symbol

The NAND gate is essentially a NOT-AND gate, equivalent to an AND gate followed by a NOT gate. The output of a NAND gate is true if any of its inputs are false. The symbol is an AND gate with a small circle on the output terminal, representing inversion.

Figure 2 depicts the NAND logic gate symbol, and Table 2 shows its truth table:

Table 2: NAND gate truth table

OR Logic Gate

Figure 3: OR gate logic symbol

The OR gate is an electronic circuit that outputs true (1) if one or more of its inputs are true. A plus (+) sign is used to represent the OR operation.

Figure 3 illustrates the OR logic gate symbol, and Table 3 presents its truth table:

Table 3: OR gate truth table

NOR Logic Gate

Figure 4: NOR gate logic symbol

The NOR gate is a NOT-OR gate, equivalent to an OR gate followed by a NOT gate. The output of a NOR gate is false if any of its inputs are true. The symbol is an OR gate with a small circle on the output, representing inversion.

Figure 4 shows the NOR logic gate symbol, and Table 4 displays its truth table:

Table 4: NOR gate truth table