Computer ScienceNEB 2076 (old course)
What is Boolean algebra ? Describe AND and NAND gates with logic symbol, truth table and Venn diagram. [4+6]
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Boolean Algebra
Boolean algebra is a branch of mathematics that deals with logical operations and binary variables. It was developed by George Boole in the 19th century and is fundamental in computer science, digital electronics, and logic design. Boolean algebra uses binary values (0 and 1) to represent logical states such as False and True, Off and On, or Low and High. The three basic operations in Boolean algebra are AND, OR, and NOT, which are used to construct more complex logical expressions.
AND Gate
The AND gate is a basic logic gate that outputs 1 (True) only when all its inputs are 1 (True). Otherwise, it outputs 0 (False).
Logic Symbol
Truth Table
| A | B | Y = A ∧ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Venn Diagram
NAND Gate
The NAND gate is a universal logic gate that performs the NOT operation on the output of an AND gate. It outputs 0 (False) only when all its inputs are 1 (True). Otherwise, it outputs 1 (True).
Logic Symbol
Truth Table
| A | B | Y = A ∧ B (AND) | Y = ¬(A ∧ B) (NAND) |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
Venn Diagram
Explanation
AND Gate:
- The output is 1 only when both inputs A and B are 1.
- The Venn diagram shows the intersection of sets A and B, representing the condition where both inputs are true.
NAND Gate:
- The output is the inverse of the AND operation.
- The Venn diagram shows the complement of the intersection of sets A and B, indicating that the output is 1 unless both inputs are 1.
These gates are fundamental in designing digital circuits, combinational logic, and sequential circuits in computer systems.
Discussion
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