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3.0 THE LOGIC GATES

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Well binary is nice n easy n all but if thats all that a computer

understands then how does it go from that to a word processor or 

an entire operating system. Well we build up these complicated 

tasks using simple logic gates and boolean algebra, boolean 

algebra was created by George Boole in Ireland in the 1800's, 

wahey. The gates provide a way to make decisions and more 

complex tasks are built upon them. These gates accept input of 

Binary numbers and their output is based on the type of gate and 

what input was involved. There are three simple gates.



3.1 THE NOT GATE

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The simplest of all the gates is the NOT gate, it just takes 

a binary value of either 1 or 0 and gives back the oppossite. 

The NOT gate is symbolised by the operator '~'. Consider the 

following.



 A | Q

 ------+-------

 0 | 1

 1 | 0





 ~0 = 1

 ~1 = 0



This table shows all possible inputs and outputs of the NOT 

gate, this kind of a table is known as a 'truth table'.



3.2 THE AND GATE

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The AND gate unlike the NOT gate doesnt take just one input 

(A) it takes at least 2 (A,B), its symbol is '&'.



 A B | Q

 -------+------

 0 0 | 0

 0 1 | 0

 1 0 | 0

 1 1 | 1





 0 & 0 = 0

 0 & 1 = 0

 1 & 0 = 0

 1 & 1 = 1



As you can see from the truth table above, the output of 

a AND gate is only equal to 1 when both A AND B are equal 

to 1, this is the following.



If A = 0 and B = 0 then Q = 0

If A = 0 and B = 1 then Q = 0

If A = 1 and B = 0 then Q = 0

If A = 1 and B = 1 then Q = 1



3.3 THE OR GATE

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The OR gate also only takes in 2 parameters, A and B, its 

symbol is '|'



 A B | Q

 -------+------

 0 0 | 0

 0 1 | 1

 1 0 | 1

 1 1 | 1



 

 0 | 0 = 0

 0 | 1 = 1

 1 | 0 = 1

 1 | 1 = 1



The OR gate outputs a value of 1 if either A OR B OR both 

are equal to 1



If A = 0 and B = 0 then Q = 0

If A = 0 and B = 1 then Q = 1

If A = 1 and B = 0 then Q = 1

If A = 1 and B = 1 then Q = 1