Exclusive OR gate (EXOR GATE) or XOR Gate
The output of an exclusive OR gate is HIGH if its one input, but not both is HIGH. The Output of the EXOR gate is HIGH if Inputs are different (one is high and another is low) and the output is LOW when both inputs is the same (Either low or high). The Exclusive OR gate is also called as EXOR gate.
The name exclusiveOR gate is derived from the fact that the output of its is 1, only when exclusively one of its input is 1. The operation of the Exclusive –OR gate is denoted by Ꚛ. And the expression for the output of its circuit is given as
Z =A Ꚛ B =
$\overline{A}B+A\overline{B}$
(A bar.B Plus A.B bar)
The circuit of EXOR (XOR) gate
The Equivalent circuit and Symbol of EXOR (XOR) gate
The truth table of EXOR gate
The EXOr gate has only two inputs, there are no 3 or 4 input EXor gates. The operation of EXOR gate is denoted by Ꚛ (plus sign surrounded by a circle).
The circuit of the EXOR gate is also called an inequality comparator or detector because it produces output only when the two inputs are different. It means Output is 1 when inputs are not equal. It is also called anticoincidence gate. It should be noted that the same ExOR Truth table applies when adding two binary digits(bits). The main property of an EXOR gate is that can perform modulo2 addition. A 2input EXOR circuit is sometimes called a modulo2 adder or a half adder because the possible carry bit has not been taken, resulting from an addition of two preceding bits.
Three or more variable EXOR gates do not exist. When more than two variables are to be ExORed, a number of two input EXOR gates will be used. The XOR of a number of variables assumes a1 state only when an odd number of input variables assumes a 1 state.
XOR gate as an inverter
An EXOR gate can be used as an inverter by connecting one of its two input terminals to logic 1 and feeding the input sequence to be inverted to the other terminal.
If the input bit is 0, the output is, 0 Ꚛ 1 = 1 and if the input bit is 1, the output is 1 Ꚛ 1= 0. So we can say that the ExOR gate can be used as a controlled inverter. Where one of the inputs can be used to decide whether the signal at the other input signal will be inverted or not.
The ic 7486 is a TTL packaging of EXOR gates. And the 74C86 is a CMOS IC package both IC contains four EXOR gates. Highspeed CMOS IC 74HC86 contains four EXOr gates.
Exclusive NOR gate
Exclusive NOR gate is also called as EXNOR or XNOR gate. An XNOR gate is a combination of an XOR gate and a NOT gate. This circuit operates just opposite to the XOR circuit. The 4 output of this gates is HIGH if and only if its both inputs are same (either 0 or 1), and its output is LOW if inputs are different. It is also called a coincidence gate because its output is 1 only when its input coincides (0, 0 or 1, 1). It can be used as an equality detector because its output is 1 only when its inputs are equal.
Circuit Of EXNOR (XNOR) gate
Symbol and Equivalent circuit of XNOR gate
Three or more variable XNOR gates do not exist. When a number of variables are to be XNORed, a number of twoinput XNOR gates can be used. The XNOR of a number of variables assumes a 1 state, only when an even number (including zero) of input variables assumes a 0 state.
EXNOR (XNOR) Gate truth table
ExNOR gate as an inverter
An XNor gate can be used as an inverter by connecting one of two input terminals to logic 0 and feeding the input sequence to be inverted to the other terminal. If the input bit is a 1, the output is. If the input bit is 0, the output is. The XNOR of two variables A and B is the complement of the XOR of the two variables.
z = A Ꚛ B =
$AB+\overline{A}\overline{B}$
(A. B plus A bar.B bar)
The XNOR gate can be used as a controlled inverter, that is, one of its inputs can be used to decide whether the signal at the other inputs will be inverted or not. The xNOR gate can be used as a comparator too.
But the XNOR of three variables A, B, and C is not equal to the complement of the XOR of A, Band C.
The XNor of a number of variables is equal to the complement of the XOR of those variables only when the number of variables contains even.
The TTL IC 74LS266, the CMOS IC 74V266 and the highspeed CMOS IC 74HC266 is the packaging of four XNor gates in each.
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