M4: The Logic Boolean Algebra

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7 Terms

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Boolean Algebra

It is a branch of algebra that deals with binary variables that have only two possible values and logical operations.

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George Boole

Boolean Algebra was introduced by the mathematician __________ in the mid-1800s and became the mathematical foundation of digital electronics, logic circuits, and computer science.

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0 (False/LOW/OFF) or 1 (True/HIGH/ON)

What values can Boolean variables take?

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Conventional uses arithmetic (+, −, ×), Boolean uses logical operations (AND, OR, NOT).

How is Boolean Algebra different from conventional algebra?

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Boolean Algebra Laws and Properties: 

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  • Boolean function

  • truth table

A __________ is an algebraic expression consisting of Boolean variables and operations. Every Boolean function can be represented by a __________.

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  • Standard Forms:
    1. Sum of Products (SOP): Expression is a sum of AND terms.
    2. Product of Sums (POS): Expression is a product of OR terms.

  • Canonical Forms:

    1. Sum of Minterms (Σm)

    2. Product of Maxterms (M)

  • Product Terms
    A single variable or the logical product of several variables.

  • Sum Terms
    A single variable or the logical sum of several variables

  • Minterm (m)
    The logical product of all variables

  • Maxterm (M)
    The logical sum of all variables

Forms of Boolean Functions: