The agenda: Circuit Synthesis

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What are the three stages of circuit synthesis?
The three stages of circuit synthesis are:

  1. Truth Table.
  2. Applying Building Methodology.
  3. Highly Structed Boolean Function.

Minterm(m)

How do you find a minterm?
To find the minterm:

  1. Find the rows in the truth table that output a 1.
  2. For each of those rows, write the variables that are 1 and the complemented versions of the variables that are 0 as a product within parentheses.
  3. Write the final equation as a sum of the products created in the last step.

Minterm Sum-of-Product

What does SOP stand for?
SOP stands for Sum Of Products.

What is a minterm? (1)
A minterm is a specific product (AND) of each variable in a Boolean function which evaluates to 1 (true).

What are the two operations that appear in a minterm? (1)
The two operations that appear in a minterm are:

  1. Conjunction (AND).
  2. Complement (NOT).

What are the two forms a variable can appear in a minterm?
The two forms a variable can appear in a minterm are:

  1. Uncomplemented form (as itself).
  2. Complement form (negated).

What does a minterm evaluate to?
A minterm evaluates to 1, or true.

From the professor

We can't create a minterm for a row which evaluates to 0 because we wouldn't know which variable is causing the expression to evaluate to 0. Because we are using the AND operation between all variables in the row, any one of them can be 0.

What is the Sum Of Products?
The Sum Of Products is a representation of a Boolean function as a sum (OR) of several minterms.

Intuitive Understanding of SOP

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How is Sum Of Product (SOP) representative of a Boolean function ?
SOP is representative of a Boolean function by covering all possible situations that result in a positive result.

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MaxTerm (M)

How do you find a maxterm?
To find the maxterm:

  1. Find the rows in the truth table that output a 0.
  2. For each of those rows, write the variables that are 0 and the complemented versions of the variables that are 1 as a sum within parentheses.
  3. Write the final equation as a product of the sums created in the last step.

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Coming up Next:

Who are Karnaugh Maps named after?
Karnaugh Maps are named after Dr. Maurice Karnaugh.