LOGIC

GATES

INTRODUCTION TO LOGIC GATES

Boolean functions may be practically implemented by using electronic gates. The following points are important to understand.

• Electronic gates require a power supply.

• Gate INPUTS and OUTPUTS are driven by voltages having two nominal values, e.g. 0V and 5V representing logic 0 and logic 1 respectively.

• There is always a time delay between an input being applied and the output responding.

COMPUTER ARCHITECTURE

Truth tables are used to help show the function of a logic gate.

Truth tables help understand the behaviour of logic gates.

• They show how the input(s) of a logic gate relate to its output(s).

• The gate input(s) are shown in the left column(s) of the table with all the different possible input combinations. This is normally done by making the inputs count up in binary.

• The gate output(s) are shown in the right hand side column.

COMPUTER ARCHITECTURE

Truth Table Diagram

                                                                      

Creating TRUTH TABLES

Questions:

Create a truth tables for the following circuits, that have:

• 2 inputs

• 3 inputs

• 4 inputs

LOGIC GATES

• Digital systems are said to be constructed by using logic gates.

• These gates are the:

1. AND gate

2. OR gate

3. NOT gate

4. NAND gate

5. NOR gate

6. EXOR gate

7. EXNOR gate

Basic Logic Gates

BASIC LOGIC GATE - AND

The AND gate is an electronic circuit that gives a high output (1) only if all its inputs are high.  

A dot (.) is used to show the AND operation i.e. A.B.  Bear in mind that this dot is sometimes omitted i.e. AB

BASIC LOGIC GATE - AND

In this animated AND Logic example of Doors Opening and Closing, you can see that in order for the "Light" to get through the house, the front door AND the back door must be Open. 

BASIC LOGIC GATE - AND

In order for the Output of an AND Logical Function to be TRUE: input (1) AND input (2) must both be TRUE.  This is Positive Logic.

Using the Same Function --It is also correct to say: If either input (1) OR input (2) (or both) is NOT TRUE the Output Will be FALSE. This is Negative Logic.

Hint: TRUE is when the switch is closed,  applying power to the LED.  FALSE is when the switch is open,  NOT applying power to the LED)

                                  

A & B are the Input switches C is the Output

Truth Table

BASIC LOGIC GATE - OR

                                  

The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high.  A plus (+) is used to show the OR operation.

BASIC LOGIC GATE - OR

                                  

In this animated OR Logic example, you can see that in order to get light through the house: the left front door OR the right front door (or both) must be Open. 

Same example: in order to block the light through the house: the left front door AND the right front door must be Closed.

BASIC LOGIC GATE - OR

In order for the Output of an OR Logical Function to be TRUE: either  input (1) OR input (2) (or both) must be TRUE.  This is Positive Logic.  

Using the Same Function --It is also correct to say: In order for the Output to be FALSE: input (1) AND input (2) must both be FALSE. This is Negative Logic.

A & B are the Input switches C is the Output

Truth Table

BASIC LOGIC GATE - NOT

The NOT gate is an electronic circuit that produces an inverted version of the input at its output.  It is also known as an inverter.  If the input variable is A, the inverted output is known as NOT A.  This is also shown as A', or A with a bar over the top, as shown at the outputs.

Activity

Draw the circuit and truth tables for the following logical expressions that output to ‘O’:

1.(CD)’

2.A + (A + B)

3.AB + BC

4.C’ + BC

5.(A+D)(AD)’

6. A’B’(A + B)(B + B)

7.(A + C)(A’D + AD) + AC + C’

8.A(A + B) + (B + (AA)’)(A + B)

LOGIC GATES - NANDThis is a NOT-AND gate which is equal to an AND gate followed by a NOT gate.  The outputs of all NAND gates are high if any of the inputs are low. The symbol is an AND gate with a small circle on the output. The small circle represents inversion.

Activity:

Draw a circuit that shows how the NAND gate would be drawn using ONLY the basic logic gates.

LOGIC GATES - NORThis is a NOT-OR gate which is equal to an OR gate followed by a NOT gate.  The outputs of all NOR gates are low if any of the inputs are high. The symbol is an OR gate with a small circle on the output. The small circle represents inversion.

Activity:

Draw a circuit that shows how the NOR gate would be drawn using ONLY the basic logic gates.

LOGIC GATES - EXORThe 'Exclusive-OR' gate is a circuit which will give a high output if either, but not both, of its two inputs are high.  An encircled plus sign ( ) is used to show the EOR operation.

Activity:

Draw a circuit that shows how the EXOR gate would be drawn using ONLY the basic logic gates.

LOGIC GATES - EXNORThe 'Exclusive-NOR' gate circuit does the opposite to the EOR gate. It will give a low output if either, but not both, of its two inputs are high. The symbol is an EXOR gate with a small circle on the output. The small circle represents inversion.

Activity:

Draw a circuit that shows how the EXNOR gate would be drawn using ONLY the basic logic gates.