TOPIC 10 | LOGIC SYMBOLS AND FUNCTIONS

ON THIS PAGE
10.1 Identify and use the standard symbols for logic gates
10.2  Define and understand the functions of the logic gates: Including:
– NOT
– AND
– OR
– NAND
– NOR
– XOR (EOR)
– the binary output produced from all the possible binary inputs
• NOT is a single input gate
• All other gates are limited to two inputs

ALSO IN THIS SECTION
LOGIC SYMBOLS AND FUNCTIONS
USING LOGIC GATES

WHAT ARE LOGIC GATES

Logic gates are a major component of a computers hardware, there are usually thousands of logic gates in the circuits of computers. Logic gates act as a switch and control the flow of electricity through them depending on the combination of input they receive.

The types of logic gates discussed in this section are:

• NOT Gate ( represented with Ā)
• OR Gate  (represented with  A + B)
• NOR Gate
• AND Gate (represented with A x B or A · B )
• NAND Gate
• XOR Gate ( Represented with ⊕ )

Each of the various working of the logic gates can be illustrated in Truth Tables. As circuits get big and multiple logic gates or used together it is good practice to use truth tables to trace the outcomes. Most truth tables will replace the text ON and OFF with 1 and 0.

THE NOT GATE

The NOT gate is the only gate with just one input. The NOT gate simply reverses the input, if the input is ON then the OUTPUT is OFF, if the input is OFF then the output is on.

NOT GATE

The image above illustrates a NOT gate, it is the circle that symbolises the NOT and this circle is also used on other gates discussed later. Below is the truth table for the NOT gate.

NOT GATE TRUTH TABLE

The NOT gate can be represented in Boolean Algebra by placing a combining overbar over the values to pass through a NOT gate, so NOT A can be represented as Ā

THE OR GATE

The OR gate will give an output value of ON if any of the inputs are ON.

OR GATE

The OR gate can be viewed as the mathematical equivalent of addition. 
A + 0 = A
A + A = A
0 + 0 = 0
A + Ā = 1
Notably different from normal mathematics as in boolean logic the above shows the the sum of a variable will equal the variable, for example 1 + 1 = 1

OR GATE TRUTH TABLE

THE NOR GATE

The NOR Gate or NOT OR Gate will have an output if none of the inputs are 1. The NOR gate has a circle on the output to define the NOT part of the gate. You can see this as the opposite of an OR gate.

NOR GATE TRUTH TABLE

NOR GATE

THE AND GATE

The AND gate will only give an output when both inputs are ON, in other works input one AND input two need to be ON to make the output ON.

AND GATE

AND GATE TRUTH TABLE

The AND gate can be viewed are the mathematical equivalent to multiplication.
A x 0 =  0
A x 1 = A
​A x A = A
A x Ā = 0

THE NAND GATE

The NAND Gate or NOT AND Gate will have an output when the two inputs are not ON. Or with a three input NAND gate when all 3 inputs are not ON.

NAND GATE TRUTH TABLE

THE NAND GATE

THE XOR GATE

The XOR gate or eXclusive OR will only produce an output it the two inputs are different values.

XOR TRUTH TABLE

THE XOR GATE

THE XNOR GATE

The exclusive not or will be 1 if both input values are the same. 

LOGIC GATE QUESTIONS

1: What does the NOT gate do?
A. Outputs true if both inputs are true
B. Inverts the input signal
C. Outputs true if either input is true
D. Outputs true if both inputs are false

2: In an AND gate, the output is true when:
A. Any one of the inputs is true
B. None of the inputs are true
C. Both inputs are true
D. Both inputs are false

3: Which gate will have a true output when either of its inputs is true?
A. NOT
B. AND
C. OR
D. NAND

4: What is the output of a NAND gate when both inputs are true?
A. True
B. False
C. The same as the input
D. Can't be determined

5: The NOR gate outputs true when:
A. Both inputs are true
B. Either input is true
C. Neither input is true
D. Inputs are different

6: An XOR (Exclusive OR) gate outputs true if:
A. Both inputs are true
B. Both inputs are false
C. The inputs are different
D. The inputs are the same

7: Which statement is true about the OR gate?
A. It outputs false only when both inputs are false
B. It always outputs true
C. It outputs true only when both inputs are true
D. It inverts the input signal

8: If an AND gate has an input of 1 and 0, the output will be:
A. 1
B. 0
C. The same as the input
D. Can't be determined

9: In a NAND gate, if one input is 0 and the other is 1, the output will be:
A. 1
B. 0
C. The same as the input
D. Inverted

10: Which gate behaves like an OR gate followed by a NOT gate?
A. AND
B. XOR
C. NOR
D. NAND