Saturday, March 2, 2013

Simple Gates-NOT, AND and OR

Simple Gates-NOT, AND and OR

The circuits of a computer may contain millions of components, but most of this is made up by repeating a few different gates.

NOT GATE (INVERTER)

(The output is NOT the same as the input.)

Functions of NOT gate in words: a logic gate with one input. The output is logic 0 if the input is logic 1 and is logic 1 if the input is logic 0.

Truth table for NOT gate

Input

Output

0

1

1

0

Fig 3 Truth table for a NOT gate

Note: The operation carried out by a NOT gate is referred to as inverting.

AND GATE

(The output is 1 only when A AND B are 1)

Functions of AND gate in words: a logic gate with two or more inputs. The output is logic 1 when both (or all) the inputs are logic 1; otherwise the output is logic 0.

Truth table for AND gate (two inputs)

Input

Input

Output

A

B

0

0

0

0

1

0

1

0

0

1

1

1

Fig 4 Truth table for an AND gate

OR GATE

(Output is 1 when A OR B is 1-this includes the case when both of A and Bare 1.)

Function of OR gate in words: a logic gate with two or more inputs. The output is logic 1 when anyone of the inputs is logic 1; the output is logic 0 when both (or all) the inputs are logic 0.

Truth table for OR gate (two inputs)

Input

Input

Output

A

B

0

0

0

0

1

1

1

0

1

1

1

1

Fig 5 Truth table for an OR gate

Worked questions

1 Draw a truth table for the following logic diagram. Show the logic values at D, E, F and G.

Digital Logic 3

 

Answer: The truth table is as follows:

A

B

C

D

E

P

G

0

0

0

1

1

0

1

0

0

1

1

1

0

1

0

1

0

0

0

0

0

0

1

1

0

0

1

1

1

0

0

1

1

0

1

1

0

1

1

1

0

1

1

1

0

0

1

0

1

1

1

1

0

1

1

1

Notes: 1 A,B,C, are the inputs. The table must show all eight combinations of these.

2 D is obtained by inverting values of B.

E is obtained from the A and D columns using the truth table for OR.

F is obtained from the B and C columns using the truth table for AND.

G is obtained from the E and F columns using the truth table for OR.

2 If A = 10011, B = 10101 and C = 11001 find (A OR B) AND (NOT C), carrying out the operations on corresponding bits of A, B and C.

Answer: A OR B= 10111

NOT C=00110

∴ (A OR B) AND (NOT CI=10111 AND 00110 =00110

Note: Detail of A OR B: 10011

10101

10111

The bits are OR-ed one pair at a time-a bit from A with a bit from B.

3 A line to a computer is to be in use when a printer or a disc unit are free and when the computer is also free. Draw a logic diagram for a circuit which will ensure that this is so.

Assume that when a device is free it inputs 1 to the circuit, and 0 when it is not free. Assume when the circuit outputs 1 the line is in use.

Answer: The circuit is:

Digital Logic4

4 Draw a truth table for the following circuit:

Digital Logic5

Answer; The truth table is as follows:

A

B

c

NOTB

Output

0

0

0

1

0

0

0

1

1

0

0

1

0

0

0

0

1

1

0

0

1

0

0

1

0

1

0

1

1

1

1

1

0

0

0

1

1

1

0

0