What are the logical operators used in Boolean Algebra ?Name them with their symbol and draw them with truth tables
Answers
Answer:
Logic Function Boolean Notation
AND A.B
OR A+B
NOT A
NAND A .B
NOR A+B
EX-OR (A.B) + (A.B) or A ⊕ B
EX-NOR (A.B) + (A.B) or A ⊕ B
Explanation:
2-input AND Gate
For a 2-input AND gate, the output Q is true if BOTH input A “AND” input B are both true, giving the Boolean Expression of: ( Q = A and B ).
Symbol Truth Table
boolean algebra AND gate truth table A B Q
0 0 0
0 1 0
1 0 0
1 1 1
Boolean Expression Q = A.B Read as A AND B gives Q
Note that the Boolean Expression for a two input AND gate can be written as: A.B or just simply AB without the decimal point.
2-input OR (Inclusive OR) Gate
For a 2-input OR gate, the output Q is true if EITHER input A “OR” input B is true, giving the Boolean Expression of: ( Q = A or B ).
Symbol Truth Table
boolean algebra OR gate truth table A B Q
0 0 0
0 1 1
1 0 1
1 1 1
Boolean Expression Q = A+B Read as A OR B gives Q
NOT Gate (Inverter)
For a single input NOT gate, the output Q is ONLY true when the input is “NOT” true, the output is the inverse or complement of the input giving the Boolean Expression of: ( Q = NOT A ).
Symbol Truth Table
boolean algebra NOT gate truth table A Q
0 1
1 0
Boolean Expression Q = NOT A or A Read as inversion of A gives Q
The NAND and the NOR Gates are a combination of the AND and OR Gates respectively with that of a NOT Gate (inverter).
2-input NAND (Not AND) Gate
For a 2-input NAND gate, the output Q is NOT true if BOTH input A and input B are true, giving the Boolean Expression of: ( Q = not(A AND B) ).
Symbol Truth Table
NAND gate truth table A B Q
0 0 1
0 1 1
1 0 1
1 1 0
Boolean Expression Q = A .B Read as A AND B gives NOT-Q
2-input NOR (Not OR) Gate
For a 2-input NOR gate, the output Q is true if BOTH input A and input B are NOT true, giving the Boolean Expression of: ( Q = not(A OR B) ).
Symbol Truth Table
NOR gate truth table A B Q
0 0 1
0 1 0
1 0 0
1 1 0
Boolean Expression Q = A+B Read as A OR B gives NOT-Q
As well as the standard logic gates there are also two special types of logic gate function called an Exclusive-OR Gate and an Exclusive-NOR Gate. The Boolean expression to indicate an Exclusive-OR or Exclusive-NOR function is to a symbol with a plus sign inside a circle, ( ⊕ ).
2-input EX-OR (Exclusive OR) Gate
For a 2-input Ex-OR gate, the output Q is true if EITHER input A or if input B is true, but NOT both giving the Boolean Expression of: ( Q = (A and NOT B) or (NOT A and B) ).
Symbol Truth Table
Ex-OR gate truth table A B Q
0 0 0
0 1 1
1 0 1
1 1 0
Boolean Expression Q = A ⊕ B
2-input EX-NOR (Exclusive NOR) Gate
For a 2-input Ex-NOR gate, the output Q is true if BOTH input A and input B are the same, either true or false, giving the Boolean Expression of: ( Q = (A and B) or (NOT A and NOT B) ).
Symbol Truth Table
Ex-NOR gate truth table A B Q
0 0 1
0 1 0
1 0 0
1 1 1
Boolean Expression Q = A ⊕ B
Summary of 2-input Logic Gates
The following Truth Table compares the logical functions of the 2-input logic gates above.
Inputs Truth Table Outputs For Each Gate
A B AND NAND OR NOR EX-OR EX-NOR
0 0 0 1 0 1 0 1
0 1 0 1 1 0 1 0
1 0 0 1 1 0 1 0
1 1 1 0 1 0 0 1
The following table gives a list of the common logic functions and their equivalent Boolean notation.