XOR gate

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This article is about XOR in the sense of an electronic logic gate (e.g. CMOS 4030). For XOR in the purely logical sense, see Exclusive disjunction. For other uses of the term, see XOR (disambiguation).
INPUT
A   B		 OUTPUT
A XOR B
0 0 0
0 1 1
1 0 1
1 1 0

The XOR gate (sometimes EOR gate) is a digital logic gate that implements exclusive disjunction - it behaves according to the truth table to the right. 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.

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.

Contents

[edit] 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
'Military' XOR Symbol
'Rectangular' XOR Symbol
'Rectangular' XOR Symbol


A XOR B= A.(/B) +(/A).B

       where /A represents NOT A

[edit] 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  Input A2
 5  Input B2
 6  Output Q2
 7  VG
 8  Input A3
 9  Input B3
 10 Output Q3
 11 Input AA
 12 Input B4
 13 Output Q4
 14 VCC

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

[edit] Alternatives

If no specific XOR gates are available, one can be made from four NAND or five NOR gates in the configurations shown below.

XOR gate constructed using only NAND gates
XOR gate constructed using only NAND gates
XOR gate constructed using only NOR gates
XOR gate constructed using only NOR gates


[edit] 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.

three ones XORed simultaneously

A second interpretation is also possible, based on both the linguistic sense of the term "exclusive OR" and the IEC symbol for an XOR gate (see right). This interpretation states that the output is 1 when one or other of the inputs, exclusively, is 1. The "=1" in the IEC symbol implies the same thing. However, the IEC symbol was not intended to be modified by adding further inputs, and becomes invalid when this is done. This interpretation is rarely used in electronics, since parity generators and adders are in more common use than "1 of n" detectors.

[edit] See also

v • d • e
Logical connectives
OR · ← · → · NAND
AND · ↛ · ↚ · NOR

[edit] References

  1. ^ "exclusive OR n." The Concise Oxford English Dictionary, Eleventh edition revised . Ed. Catherine Soanes and Angus Stevenson. Oxford University Press, 2006. Oxford Reference Online. Oxford University Press. Birmingham City Council. 27 May 2007 [1]