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Boolean Logic

4.2 Boolean logic

 

 

Presumably the 3 inputs is to a circuit but the circuit could consist of, say, just one gate, theoretically.

 

On this page: [ basics | truth tables | expressions ]

Basic Gates

Candidates need to know the basic operators and, or, not, nand, nor and xor, their symbols , how to express them in conventional notation and their truth tables (with a maximum of three inputs).

Boolean expressions can also be written in words:

(A xor not B)

Truth Tables

and

or

not  

A

B

A and B

A

B

A or B

A

not A

0

0

0

0

0

0

0

1

0

1

0

0

1

1

1

0

1

0

0

0

1

1

1

1

1

1

1

1

 

 

nand

nor

xor

A

B

A nand B

A

B

A nor B

A

B

A xor B

0

0

1

0

0

1

0

0

0

0

1

1

0

1

0

0

1

1

1

0

1

1

0

0

1

0

1

1

1

0

1

1

0

1

1

0

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Boolean expressions

You can be asked to construct Boolean expressions using the above operators, for example:

This expression is equivalent to (A xor not B) and (C nor D).

The value of a Boolean expression such as can be given in a truth table:

Input

Input

intermediate

Output

a

b

not b

a xor not b

0

0

1

1

0

1

0

0

1

0

1

0

1

1

0

1

Complete the truth table for

Input

Input

Output

c

d

c nor d

     
     
     
     

Complete the truth table for the whole expression

Input

Input

Input

Input

   

Output

a

b

c

d

a xor not b

c nor d

(a xor not b) and (c nor d)

             
             
             
             
             
             
             
             

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related: [ Topic 4 home | next: Simplifying Boolean expressions ]

About logic symbols, operators and truth tables.


 
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