LOGIC GATES A Logic Gate is an elementary building block of a digital circuit. Most Logic Gates have two inputs and one output. At any given moment, every terminal is one of the two binary conditions LOW (0) or HIGH (1) represented by different voltage levels. In most logic gates, low state is approximately zero volt (0 V), while the high state is approximately five volts positive (+5 V). Basic logic circuits with one or more inputs and only one output are known as gates
Representing Logic Functions There are several ways of representing logic functions Symbol to represents the gates Truth tale Boolean algebra
Logic expression of symbol: input variables are A, B and the output variable is Y, then the logic expression for particular gate.
Truth Table: Truth table is table, which represents all the possible values of logical variable/statements along with all the possible results of given combinations of values.
Boolean algebra: it is Boolean expression for particular gate.
Basically logic gates are OR gate, AND gate, NOT gate, NOR gate, NAND gate and XOR gate.
OR – GATE
OR gate symbol is
Boolean expression is A+B (“A or’ d with B”)
Logic expression: Input variable are A,B and the output variable is Y, then the logic expression for OR gate is Y = A+B.
Circuit diagram:
Truth table: Input (A) Input (B) Output (Y= A+B) 0 0 0
0 1 1 1 0 1
1 1 1
This circuit will give high output (1), if any input is high (1) , otherwise the output is low (0)
AND – GATE
OR gate symbol is
Boolean expression is A+B (“A and with B”)
Logic expression: Input variable are A, B and the output variable is Y, then the logic expression for OR gate is Y = A.B.
Circuit diagram:
Truth table: Input (A) Input (B) Output (Y= A.B) 0 0 0
0 1 0 1 0 0
1 1 1
This circuit will give high output (1), if both inputs is high (1), otherwise the output is low(0)
NOT – GATE
OR gate symbol is Y A
Boolean expression is A invert
Logic expression: Input variable is A and the output variable is Y, then the logic expression for NOT gate is Y A
Circuit diagram:
Truth table: Input (A) Output (Y= A ) 0 1
1 0
This is the simplest gate it just inverts the input, if input is high the output will be low and conversely
NOR Gate
NOR is a combination of OR gate and NOT gate
i.e., OR gate +NOT gate = NOR gate
The NOR gate works opposite to the OR gate
Its Boolean algebra representation is Y A B
Logic Symbol:
or Y A B Y A B
Truth table:
Input (A) Input (B) Output(Y A B )
0 0 1 0 1 0
1 0 0 1 1 0
This circuit will give high output (1), if both inputs is low (0), otherwise the output is low (0)
The symbol is an OR gate with a small circle on the output. The small circle represents inversion.
NAND – Gate
NAND is a combination of AND gate and NOT gate
i.e., AND gate +NOT gate = NAND gate
The NAND gate works opposite to the AND gate
Its Boolean algebra representation is Y A.B
Logic Symbol:
or
Or
Truth table:
Input (A) Input (B) Output Y A.B 0 0 1
0 1 1
1 0 1
1 1 0
This circuit will give high output (1), if any inputs is low (0), otherwise the output is low(0) The symbol is an AND gate with a small circle on the output. The small circle represents inversion.
XOR- Gate XOR gate also refer to represented as exclusive -OR gate it is a digital logic gate with two or more inputs and one output that performs exclusive disjunction One element clearly missing from the set of Boolean operations is that of Exclusive-OR, often represented as XOR. Whereas the OR function is equivalent to Boolean addition, the AND function to Boolean multiplication, and the NOT function (inverter) to Boolean complementation, there is no direct Boolean equivalent for Exclusive-OR.
Logic Symbol:
A Y A B B
Truth Table: Input (A) Input (B) Output
Y A B 0 0 0 0 1 1 1 0 1
1 1 0
The output of an XOR gate is high (1) only when exactly one of its inputs is high (1). If both of an XOR gate's inputs are low (0), or if both of its inputs are high (1), then the output of the XOR gate is low.