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

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 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 








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 
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!
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.
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.
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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