Boolean Algebra.
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Lesson at a glance
🇬🇧 English
Key points
Important concepts
01 / 07
Learning Objectives
After this lesson, you should understand:
- Boolean values in digital circuits.
- AND, OR, NOT operations.
- Boolean laws used for simplification.
- SOP and POS forms.
- Minterm, Maxterm, and canonical forms.
02 / 07
Lesson
Boolean Algebra
Boolean algebra is used to describe and simplify digital circuits using Boolean values.
Boolean operations include:
- AND
- OR
- NOT
03 / 07
Important Concepts
Boolean Laws
Identity:
A + 0 = A
A · 1 = A
Dominance:
A + 1 = 1
A · 0 = 0
Complement:
A + A’ = 1
A · A’ = 0
Absorption:
A + AB = A
A(A+B)=A
DeMorgan:
(A+B)’ = A’B’
(AB)’ = A’+B’
04 / 07
SOP and POS
SOP means Sum of Products.
POS means Product of Sums.
05 / 07
Minterm and Maxterm
Minterm is a product term containing all variables.
Rule:
0 -> complement 1 -> normal
Maxterm is a sum term containing all variables.
Rule:
0 -> normal 1 -> complement
06 / 07
Canonical Forms
Canonical SOP uses rows where F=1 and Sigma m.
Canonical POS uses rows where F=0 and Pi M.
07 / 07
Summary
Boolean algebra provides rules to simplify digital logic expressions and represent circuits mathematically.
PRACTICE THE IDEAS
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06 questionsExercises
01QUESTION 01
Simplification
Question 1
Simplify:
F = A + A·B
02QUESTION 02
Simplification
Question 2
Simplify:
F = A(A+B)
03QUESTION 03
Simplification
Question 3
Simplify:
F = A + A’B
04QUESTION 04
SOP / POS
Classify:
A’B + AC -> SOP
(A+B’)(C+D) -> POS
05QUESTION 05
Minterm Practice
A’BC = m3
ABC’ = m6
A’B’C’ = m0
06QUESTION 06
Canonical Forms
Canonical SOP:
- Find rows where F=1
- Convert rows to minterms
- Add using OR
Canonical POS:
- Find rows where F=0
- Convert rows to maxterms
- Multiply using AND
REMEMBER WHAT MATTERS
05 cardsFlashcards
Tap a card to turn it over. Tap again to return to the question.
CARD 01 FRONTTap to reveal
What is Boolean algebra?
CARD 02 FRONTTap to reveal
What are the Boolean complement rules?
CARD 03 FRONTTap to reveal
What is SOP?
CARD 04 FRONTTap to reveal
What is POS?
CARD 05 FRONTTap to reveal
Minterm conversion rule?