Table of Contents
Which Boolean law is described by the equation A B C AB AC?
Laws of Boolean Algebra Example No1
| (A + B).(A + C) | |
|---|---|
| A.A + A.C + A.B + B.C | – Distributive law |
| A + A.C + A.B + B.C | – Idempotent AND law (A.A = A) |
| A(1 + C) + A.B + B.C | – Distributive law |
| A.1 + A.B + B.C | – Identity OR law (1 + C = 1) |
How do you simplify logic expressions?
Here is the list of simplification rules.
- Simplify: C + BC: Expression. Rule(s) Used. C + BC.
- Simplify: AB(A + B)(B + B): Expression. Rule(s) Used. AB(A + B)(B + B)
- Simplify: (A + C)(AD + AD) + AC + C: Expression. Rule(s) Used. (A + C)(AD + AD) + AC + C.
- Simplify: A(A + B) + (B + AA)(A + B): Expression. Rule(s) Used.
What is Boolean algebra explain basic Boolean law?
Boolean Algebra uses a set of Laws and Rules to define the operation of a digital logic circuit. As well as the logic symbols “0” and “1” being used to represent a digital input or output, we can also use them as constants for a permanently “Open” or “Closed” circuit or contact respectively.
What are the practical applications of Boolean logic?
Boolean logic is used to solve practical problems. Expressed in terms of Boolean logic practical problems can be expressed by truth tables. Truth tables can be readily rendered into Boolean logic circuits. Example 3.10
How to simplify this expression using Boolean algebra techniques?
Example Using Boolean algebra techniques, simplify this expression: AB + A(B + C) + B(B + C) Solution Step 1: Apply the distributive law to the second and third terms in the expression, as follows: AB + AB + AC + BB + BC Step 2: Apply rule 7 (BB = B) to the fourth term.
How do you simplify AB A B A B C?
Using Boolean algebra techniques, simplify this expression: AB + A(B + C) + B(B + C)SolutionStep 1: Apply the distributive law to the second and third terms in the expression, as follows: AB + AB + AC + BB + BC Step 2: Apply rule 7 (BB = B) to the fourth term.
What is the simplest circuit with no gates?
A wire with no gates is the simplest answer. In a real circuit there might be reasons to use a gate (your AND with both inputs P, an AND with one input P and the other pulled to 1, and OR with both inputs P, an OR with one input P and the other pulled to 0, gates with Schmitt-trigger inputs, ..) but that’s a topic for the Electronicssite, not here.