# Uses for gate expressions, Nor and Xor

I'm not generally confused by Electronic Engineering, but Nor and Xor are the Gate expressions that like to break that Rule. I can't find proper answers to this question, as they are either: Too Complex. Or too Uninformative.

No and Yes, I and O are quite simple, but i stumbled across the two extra expressions I've never heard of, Nor and Xor. I'm quite new to this kind of stuff, so Nor and Xor are also new, and quite confusing. Some clarification on the uses of Nor and Xor would be appreciated.

• Not being critical of the current answers, but I think rather than a simple logic table you might be looking for practical uses? The first one that comes to mind for an XOR gate is an edge detector but I'm sure there's plenty more that maybe someone can enumerate on. – PeterJ Dec 23 '14 at 12:33
• An XOR is handy in a circuit to be used to as an invert / non-invert selector for one signal that passes through the gate with the second input being the select signal. A series of XOR gates can also be used to generate a parity signal across a bus of other signals. – Michael Karas Dec 23 '14 at 14:20
• A pair of NOR gates can be used to create a cross coupled latch circuit that can be set and cleared with high active pulse inputs. – Michael Karas Dec 23 '14 at 14:22

Truth tables:

NOR (NOT-OR) is more or less like NAND:

0 NOR 0 = NOT(0 OR 0) = NOT(0) = 1
0 NOR 1 = NOT(0 OR 1) = NOT(1) = 0
1 NOR 0 = NOT(1 OR 0) = NOT(1) = 0
1 NOR 1 = NOT(1 OR 1) = NOT(1) = 0


XOR emits 1 when the two inputs differ. You can consider this as binary addition without carry.

A XOR B = (NOT(A) AND B) OR (A AND NOT(B))

0 XOR 0 = 0
0 XOR 1 = 1
1 XOR 0 = 1
1 XOR 1 = 0


There is one special thing about the NOR gate. It (along with NAND) is what is called universal gates. That is, any other gate (AND, OR, NOT, etc.) can be implemented using just NOR gates. I think this picture shows why:

So, as far application is concerned this is the main thing. For Ex-OR, it is commonly used as a state toggle or a buffer. If you look at X-OR truth table:

You will see that if I set one input to zero it acts as a buffer. If my input is 0, then output is 0 and if my input is 1 the output is also 1 (buffer - output same as input).

On the other hand if I set one of my inputs to 1, then it acts as a toggle. If my input is 1, I get 0 and if my input is 0 my output is 1.

Why are buffers used? In digital circuits it is primarily used to introduce some time delay. Toggling - well though NOT gate does the same, it is advantageous to use X-Or because by just changing the first input 1/0 (Toggle/Buffer) can be achieved.

NOR stands for "not OR", which you can think of as OR with the output inverted:

In 1   In 2    OR   NOR
----   ----   ---   ---
0      0     0     1
0      1     1     0
1      0     1     0
1      1     1     0

XOR stands for "exclusive OR". There are several ways to think of that. The name suggests OR, but not when both inputs are equal. You can also think of it as indicating difference in the two inputs. No matter how you think about it, XOR is:

In 1   In 2   XOR
----   ----   ---
0      0     0
0      1     1
1      0     1
1      1     0

They are types of logic gate:

NOR - Negated OR (Neither one nor the other)

XOR - eXclusive OR (One or the other, but not both)