4.2.4 : Nor

What if we want the opposite of OR? We can apply a NOT operator on an OR operator and form NOT OR. However, this can get clunky using two operators. This is where the NOR operator comes in. NOR combines the two operators, NOT and OR, into one. Just like english we want neither x NOR y to be true. Below shows the truth table set up just as before, 00, 01, 10, 11.

Notation: x NOR y

x	y	x NOR y
0	0	1
0	1	0
1	0	0
1	1	0

{ "width":312, "height":108, "showToolbox":false, "devices":[ {"type":"Toggle","id":"dev0","x":108,"y":12,"label":"X"}, {"type":"Toggle","id":"dev1","x":108,"y":60,"label":"Y"}, {"type":"DC","id":"dev2","x":52,"y":36,"label":"DC"}, {"type":"NOR","id":"dev3","x":164,"y":36,"label":"NOR"}, {"type":"LED","id":"dev4","x":220,"y":36,"label":"LED"} ], "connectors":[ {"from":"dev0.in0","to":"dev2.out0"}, {"from":"dev1.in0","to":"dev2.out0"}, {"from":"dev3.in0","to":"dev0.out0"}, {"from":"dev3.in1","to":"dev1.out0"}, {"from":"dev4.in0","to":"dev3.out0"} ] }

Currently, I can't seem to find the real mathematical similarities to NOR. NOR does have some other interesting properties. Also, I felt bad about not giving another venn diagram.

A Universal Gate

As mentioned above, NOR has some very interesting properties. The most important of which is that it's a universal gate. What is a universal gate, you may ask. A universal gate is a gate that can make other gates. I can use a NOR gate to create a NOT, OR, and AND gate. This means, I can replace all these gates with NOR and solve any boolean expression with only NOR gates. Below I sketched out how to do each gate. Make the truth table for each. Don't just memorize what these look like, understand why they work.

x	x NOR x	NOT x
0	1	1
1	0	0

x	y	(x NOR y) NOR (x NOR y)	x OR y
0	0	0	0
0	1	1	1
1	0	1	1
1	1	1	1

x	y	(x NOR x) NOR (y NOR y)	x AND y
0	0	0	0
0	1	0	0
1	0	0	0
1	1	1	1

Practice Problems

If y is false and (x NOR y) is true, what is x?

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