XOR gate

The XOR gate (sometimes EOR gate) is a digital logic gate that implements exclusive disjunction - it behaves according to the truth table above. A HIGH output (1) results if one, and only one, of the inputs to the gate is HIGH (1). If both inputs are LOW (0) or both are HIGH (1), a LOW output (0) results.

XOR gate is short for exclusive OR. This means that precisely one input must be 1 (true) for the output to be 1 (true). A way to remember XOR is "one or the other but not both."

This function is addition modulo 2. As a result, XOR gates are used to implement binary addition in computers. A half adder consists of an XOR gate and an AND gate.

Symbols

There are two symbols for XOR gates: the 'military' symbol and the 'rectangular' symbol. For more information see Logic Gate Symbols.

'Military' XOR Symbol

'Rectangular' XOR Symbol

The XOR gate with inputs A and B implements the logical expression .

Hardware description and pinout

XOR gates are basic logic gates, and as such they are recognised in TTL and CMOS ICs. The standard 4000 series CMOS IC is the 4070, which includes four independent two-input XOR gates. The 4070 replaces the less reliable 4030, but keeps the pinout. The pinout diagram is as follows:

 1  Input A1
 2  Input B1
 3  Output Q1
 4  Output Q2
 5  Input A2
 6  Input B2
 7  VG
 8  Input A3
 9  Input B3
 10 Output Q3
 11 Output Q4
 12 Input A4
 13 Input B4
 14 VCC

This device is available from most semiconductor manufacturers such as NXP. It is usually available in both through-hole DIL and SOIC format. Datasheets are readily available in most Datasheet Databases.

Alternatives

If no specific XOR gates are available, one can be constructed from other available gates. An XOR gate can be trivially constructed from an XNOR gate followed by a NOT gate. If we consider the expression , we can construct an XOR gate directly using AND, OR and NOT gates. However, this approach requires five gates of three different kinds.

An XOR gate can be made from four NAND or five NOR gates in the configurations shown below. In fact, both NAND and NOR gates are so-called "universal gates," and any logical function can be constructed from either NAND logic or NOR logic alone.

XOR gate constructed using only NAND gates.

XOR gate constructed using only NOR gates.

More than two inputs

The XOR operation is a binary operation and is therefore defined only for two inputs.^[1] It is nevertheless common in electronic design to talk of "XORing" three or more signals.

The most common interpretation of this usage is that the first two signals are fed into an XOR gate, then the output of that gate is fed into a second XOR gate together with the third signal, and so on for any remaining signals. The result is a circuit that outputs a 1 when the number of 1s at its inputs is odd, and a 0 when the number of incoming 1s is even. This makes it practically useful as a parity generator or a modulo-2 adder.

See also

• Exclusive or
• XNOR gate
• Boolean algebra (logic)
• Logic gates

v • d • e Logical connectives Tautology ( ) NAND ( ) · Converse implication ( ) · Implication ( ) · OR ( ) Negation ( ) · XOR ( ) · Biconditional ( ) · Proposition NOR ( ) · Nonimplication ( ) · Converse nonimplication ( ) · AND ( ) Contradiction ( )

References