Binary Logic Gates

Interactive Logic Concepts

Binary logic is a very simple concept, often associated with a lot of unnecessarily complicated explanations which can make it seem far more difficult to understand than it really is. So here is a nice click-and-play demo;

Yellow represents a "1", or "on".
Grey represents a "0", or "off".

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Click on the inputs on the left, to set their output on the right.

All seven logical gates are: OR AND NOT NAND NOR XOR XNOR

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Logical OR Gate

The Logical OR gate will emit a "1" if either (or both) of its inputs are "1".

Input 1 Input 2 Output 0 0 0 0 1 1 1 0 1 1 1 1

OR is represented with the symbol above, or in code, most often as "A || B", or sometimes as "A | B".

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Logical AND Gate

The Logical AND gate will only emit a "1" if both its inputs are "1".

Input 1 Input 2 Output 0 0 0 0 1 0 1 0 0 1 1 1

Like OR, AND is represented with the symbol above, or in code, most often as "A && B", or "A & B", though the latter can also (in the UNIX shell) be interpreted as "run A in the background, and immediately start B".

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Logical NOT Gate

The Logical NOT gate will reverse its input.

Input Output 0 1 1 0

In most languages, the "!" symbol represents NOT. So, "a = !b" assigns the opposite of b to a.

Logical NAND Gate

The Logical NAND gate is an AND gate followed by a NOT gate. It will emit a 1 unless its inputs are both 1. The circle after the AND symbol indicates the NOT being performed after the AND.

Input 1 Input 2 Output 0 0 1 0 1 1 1 0 1 1 1 0

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Logical NOR Gate

The Logical NOR Gate is an OR gate followed by a NOT gate. It will emit a "1" only if both its inputs are "0". The circle after the OR symbol indicates the NOT being performed after the OR.

Input 1 Input 2 Output 0 0 1 0 1 0 1 0 0 1 1 0

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Logical XOR Gate

The Logical XOR (eXclusive OR) gate will emit a "1" if neither of its inputs are the same.

Input 1 Input 2 Output 0 0 0 0 1 1 1 0 1 1 1 0

Because of its transparent reversibility, XOR is often used in cryptography. You can XOR the plaintext with a one-time-pad to produce a cyphertext. The recipient can XOR the cyphertext with the one-time-pad to retrieve the plaintext.

For example:
0110 0101 0111 1011 (plaintext - 25,979, the original message)
1010 1101 1101 1001 (onetimepad - 44,505, a shared secret)
---- ---- ---- ---- XOR
1100 1000 1010 0010 (cyphertext - 51,362, the encoded message)

Which translates back to:

1100 1000 1010 0010 (cyphertext - 51,362)
1010 1101 1101 1001 (onetimepad - 44,505)
---- ---- ---- ---- XOR
0110 0101 0111 1011 (plaintext - 25,979)

So the original plaintext is retrieved from the encoded message and the shared secret.

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Logical XNOR Gate

The Logical XNOR Gate is an XOR gate followed by a NOT gate. It will emit a "1" only if both its inputs are the same. The circle after the XOR symbol indicates the NOT being performed after the XOR.

Input 1 Input 2 Output 0 0 1 0 1 0 1 0 0 1 1 1

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If you found this interesting or useful, you might want to check out the Shell Scripting Tutorial, Shell CheatSheet (or the PDF Version), and/or my *nix Shell Blog.

Wow! Within 5 days (created Mon 3/9/07), this is already #3 on Google for Binary Logic Gate.

And then again, with Dominoes:

Here is an OR, AND, and XOR gate, demonstrated with Dominoes!: