2) Boolean Algebra and Logic Gates

Question 1

What is Boolean Algebra?

Answer 1

Boolean algebra is a formal notation for describing logical relations. AND, OR & NOT.

Question 2

NOT Gate

Answer 2

Q = ¬A (NOT A)

Input Output
A NOT A
1 0
0 1

Question 3

AND Gate

Answer 3

Q = A . B (A AND B)

A            B            Q
0            0             0
0             1             0
1              0            0 
1              1              1

Question 4

OR Gate

Answer 4

Q = A + B (A OR B)

A             B            Q
0             0            0
0             1              1
1              0             1
1              1              1

Question 5

XOR

Answer 5

Q = A ⊕ B (A XOR B)
Q = (A . ̅B) + (Ā . B)

“Exclusive OR” - True when one input or the other is True, not both.

A           B             Q
0           0              0
0           1               1
1            0              1
1            1               0

Question 6

NOR

Answer 6

Q = (A+B) ̅ NOT (A OR B)

A           B              Q
0           0               1           
0            1               0
1             0              0
1             1               0

Question 7

NAND

Answer 7

Q = (A.B) ̅ NOT (A AND B)

A           B             Q
0           0             1
0           1              1
1            0             1
1            1              0

Question 8

Order of operations

Answer 8

1. Brackets
2. NOT ( ̅ or ¬)
3. AND, NAND ( . )
4. OR, NOR, XOR ( + or ⊕)

A.B+C
(A.B)+C