digital-logic
I've just started studying computer engineering, and I'm having some doubts regarding the behavior of the XOR gate.
I've been projecting circuits with Logisim, whose XORs behave differently from what I've learnt. To me, it should behave as a parity gate, giving a high output whenever the inputs receives an odd combination. It doesn't, though, for more than two inputs. How should it behave?
I also read in a book that XOR gates are not produced with more than two inputs. Is that correct? Why?
The circuit looks fine
The XOR table should be
A B Q
0 0 0
0 1 1
1 0 1
1 1 0
How about this?
simulate this circuit – Schematic created using CircuitLab
To light the lamp, one of the switches must be closed and the other open. Note that if both switches are closed, a lot of power will be wasted in the resistors but the light will be fully off. Note further that one may have to use a very small bulb and may have to use a higher voltage or reduce the resistors to get much light, but one should ensure that the voltage squared divided by the resistance does not exceed the resistor's power rating (for example, if you used 12 volts and 22 ohms, you would need to use 5-watt resistors). Alternatively you could replace the resistors with light bulbs and shelter them so their light isn't visible.
If you want a transistor circuit, here's half of a circuit I designed for my parents' car some decades back when I was about eight (I don't remember the actual resistor values; the transistors were some sort of TO-3 package and not 3906's; the components given should be suitable for demonstration purposes--the real one used a lamp rather than an LED and resistor). An electrical engineering grown-up friend helped with the design, but I designed the overall concept.
The left-side input is wired to one of the turn signal flashers on the car; the right-side input is wired to the brake light. The lamp is the left light of a trailer. The right-side flasher and trailer lamp are wired similarly. Note that positive is on the bottom. Your son's challenge is to figure out what the diodes on the bottom are for (consider the above description of what the circuit was connected to).
Best Answer
There are different points of view regarding how an exclusive-OR gate with more than two inputs should behave. Most often such an XOR gate behaves like a cascade of 2-input gates and performs an odd-parity function. However, some people interpret the meaning of exclusive-OR more literally and say that the output should be a 1 if and only if exactly one of the inputs is a 1. I do seem to recall that Logisim uses the latter interpretation, and somewhere in my rusty memory I have seen it in an ASIC cell library. One of the the international standard symbols for an XOR gate is a rectangle labelled with
=1which seems to be more consistent with the "1 and only 1" definition.EDIT: The definition of exclusive-OR as "1 and only 1" is uncommon but it can be found. For example, IEEE-Std91a-1991 gives the symbol for the exclusive-OR on p. 62 with the note: "The output stands at its 1-state if one and only one of the two inputs stands at its 1-state." For more than 2 inputs the standard recommends using the "odd parity" symbol instead. Web sites that discuss this confusing situation include XOR: The Interesting Gate and gate demos at TAMS. A google search will also turn up sites that claim that, strictly speaking, there is no such thing as an XOR gate with more than two inputs.