Boolean Algebra - 1

Parentheses override the default precedence of logical operators, forcing evaluation of enclosed expressions first. This allows precise control over evaluation order.

The OR operator returns true if at least one of its operands is true. Unlike AND, which requires all operands to be true.

Option D evaluates NOT (15 > 15). Since 15 > 15 is false (not greater than), NOT false = true. The other options all evaluate to false.

Yes, the output of EX-NOR gate is 1 when both the options 3 and 4 follow.
Yes, the output of EX-NOR gate is 1 when both the options 3 and 4 follow.

F = A.A.B + A'. B' = 0 + A' B' = A'.B'

This is not a combinational circuit because its output depends on the previous output.
This is not a combinational circuit because its output depends on the previous output.

The AND gate outputs true only when all input expressions are true. If any input is false, the output is false.

Boolean algebra is the mathematical foundation for digital electronics, used to analyze and design digital circuits that operate with binary values (0 and 1).

In Boolean algebra, the expression x · 0 (x AND 0) always equals 0. This is known as the null law or annihilator property - anything AND 0 is 0.

This demonstrates the distributive property in Boolean algebra: x AND (y OR z) = (x AND y) OR (x AND z). The operation distributes over OR just like in regular algebra.

De Morgan's theorem states that the complement of a product (AND) equals the sum (OR) of the complements. The dual form is (x + y)' = x' · y'.

By De Morgan's theorem, the complement of an AND operation equals the OR of the complements. Thus (x · y)' = x' + y'.

A truth table lists all possible combinations of input values and the corresponding output value for a Boolean expression. This completely specifies the expression's behavior.

Truth tables provide a systematic method to verify all Boolean laws by exhaustively listing every possible input combination and the corresponding output, allowing us to prove identities like AND, OR, and complement properties.

(x + y)' = x' y' is the first of De Morgan's two laws, which states that the complement of a sum (OR operation) equals the product (AND operation) of the individual complements. This is a fundamental theorem used to simplify Boolean expressions.