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GCSE     Logic     Algebra     >Gates<     Latch     NAND Array     Schmitt NOT     Truth Tables    

Logic Gates


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  GCSE    Combinational Logic  0 of 56    Question 191    Boolean AND Symbol 
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Logic Gates are digital switching circuits that obey simple rules.
The inputs and outputs are LOW ( 0 ) or HIGH ( 1 ) and should never float halfway between.

A LOW signal is a voltage less than half the power supply, usually close to zero.
A HIGH signal 
is a voltage more than half the power supply, usually close to five volts ( or 3.3V in low voltage logic ).
Never leave inputs unconnected. They float, act as an antenna, and pick up every noise signal in range.

AND NAND OR NOR XOR XNOR NOT
Two Input AND Gate
A AND B
Two Input NAND Gate
A NAND B
Two Input  OR Gate-or.gif
A OR B
Two Input NOR Gate
A NOR B
Two Input XOR Gate
A XOR B
Two Input XNOR Gate
A XNOR B
One Input NOT Gate
Q = NOT A
Two ones give a one.
Anything else gives 0.
Two ones give a 0.
Anything else gives 1.
Two zeros give a 0.
Anything else gives 1.
Two zeros give a 1.
Anything else gives 0.
Equal inputs give a 0. Equal inputs give a 1. Input is inverted.
A B   Q
0 0   0
0 1   0
1 0   0
1 1   1
A B   Q
0 0   1
0 1   1
1 0   1
1 1   0
A B   Q
0 0   0
0 1   1
1 0   1
1 1   1
A B   Q
0 0   1
0 1   0
1 0   0
1 1   0
A B   Q
0 0   0
0 1   1
1 0   1
1 1   0
A B   Q
0 0   1
0 1   0
1 0   0
1 1   1
A  Q
0  1
1  0


B\A 0 1
0 0 0
1 0 1
B\A 0 1
0 1 1
1 1 0
B\A 0 1
0 0 1
1 1 1
B\A 0 1
0 1 0
1 0 0
B\A 0 1
0 0 1
1 1 0
B\A 0 1
0 1 0
1 0 1
A 0 1
Q 1 0

Logic Levels

  CMOS 4000 Series Chips TTL 7400 Series Chips Commonly Used Terms
Technology Complementary Metal Oxide Semiconductor Transistor Transistor Logic  
LOW A voltage less than 0.5 of the power supply 0 to 0.8 V 0, Zero, Off, Clear, False
HIGH A voltage greater than 0.5 of the power supply 2.2 to 5 V 1, One, On, Set, True
Power Extremely low power consumption High power use compared with CMOS  
Speed Slower Faster  

Boolean Algebra

BOOLE: A mathematician called Boole invented a branch of maths for processing true and false values instead of numbers. This is called Boolean Algebra. Simple Boolean algebra is consistent with common sense but if you need to process decisions involving many values that might be true or false according to complex rules, you need this branch of mathematics. Boolean algebra was invented long before the invention of logic gates!

Logic Gate Rules

There are several types of gate. Each follows a very simple set of rules. By combining many gates in suitable ways, processing devices can be produced. A computer CPU chip can have millions of gates fabricated onto it. The table above shows several gates with two inputs. Many of these gates are also available in three, four and eight input versions.

Computers work using LOGIC. Displaying graphics such as the mouse cursor involves the XOR (Exclusive OR) operation. Arithmetic addition makes use of AND and XOR.

Truth Tables

The one line descriptions of the rules above are clearer if shown in Truth Tables. These tables show the output for all possible input conditions. The inputs are always listed in the same order (counting in binary starting from zero).

EXAMPLE: There are two inputs, A and B. Input B is inverted by the NOT gate to give X.
If A and X are both high the AND gate output will go high and the alarm will sound.

A Simple Logic Gate and Alarm System

Half Adder

Half Adder

This is one of the simplest logic circuits that does something useful. It adds two bits together.

A      B   C  S
0 plus 0 = 0  0
0 plus 1 = 0  1
1 plus 0 = 0  1
1 plus 1 = 1  0

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