










Logic Circuits






Boolean algebra is ideal for expressing the behavior of logic circuits. 





A circuit can be expressed as a logic design and implemented as a collection of individual connected logic gates. 





Fixed Logic Systems



A fixed logic system has two possible choices for representing true and false. 





Positive Logic



In a positive logic system, a high voltage is used to represent logical true (1), and a low voltage for a logical false (0). 





Negative Logic



In a negative logic system, a low voltage is used to represent logical true (1), and a high voltage for a logical false (0). 





In positive logic circuits it is normal to use +5V for true and 0V for false. 











Switching Circuits



The abstract logic described previously can be implemented as an actual circuit. Switches are left open for logic 0 and closed for logic 1. 





Two variable AND circuit X.Y












Two variable OR circuit X + Y












Four variable circuit U.V.(X + Y)












Truth Table



A truth table is a means for describing how a logic circuit's output depends on the logic levels present at the circuit's inputs. 





In the following twosinputs logic circuit, the table lists all possible combinations of logic levels present at inputs X and Y along with the corresponding output level F. 











X

Y

F = X*Y

0

0

0

0

1

0

1

0

0

1

1

1







When either input X AND Y is 1, the output F is 1. Therefore the "?" in the box is an AND gate. 














