# Boolean function - minterms - literals

• General_Sax
In summary, the conversation discussed a Boolean function represented by a circuit and asked for its expression in the form of a sum of minterms. The solution involved creating a truth table and simplifying the expression using K-maps or boolean algebra. The difference between a complement and a dual was also questioned.
General_Sax
Boolean function - minterms -- literals

## Homework Statement

(a) Describe the circuit in a form of a Boolean function F(A, B, C, D, E). Convert this
expression to the sum of products form that includes minimal number of literals, and next
express this function as a sum of minterms, namely F(A, B, C, D, E) = m(….).

xx

## The Attempt at a Solution

I wrote out a truth table for the function and have a total of 11 terms. I might as well write it out here:

F = A'B'CD'E + A'B'CDE + A'BC'DE + A'BCD'E + A'BCDE + AB'C'DE + AB'CD'E + AB'CDE + ABC'DE + ABCD'E + ABCDE

next step: Convert this expression to the sum of products form that includes minimal number of literals.

Do they want me to K-map the function, or do they want me to simplify the expression algebraically (boolean algebra obviously)?EDIT: one more question: What is the difference between a complement and a dual??

Last edited:

I have another question, and I didn't want to make another thread. My question is attached into this post.

Commutative

xy = yx

Associative

x + y = y + x

so, are they asking me to prove:

(x -> y) = ( y -> x)

and

(x -> y) + (y -> x) = (y -> x) + (x -> y)

This question is really confusing me.

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Both problems solved.

Still don't understand what the difference between a compliment and a dual is though.

## 1. What is a Boolean function?

A Boolean function is a mathematical function that takes inputs of either 1 or 0, and produces an output of either 1 or 0. It is used in digital logic and computer science to model logical operations and circuits.

## 2. What are minterms in a Boolean function?

Minterms are the product terms in a Boolean function that represent all possible combinations of inputs in which the function produces an output of 1. They are also known as standard conjunctions.

## 3. What are literals in a Boolean function?

Literals are the variables or inputs in a Boolean function that can take on the values of either 1 or 0. They can be represented by letters such as A, B, C, etc. and can also be complemented by using a bar or an overline symbol.

## 4. How are minterms and literals related in a Boolean function?

Minterms can be represented as a combination of literals, where each literal represents an input that is present in the minterm. The number of literals in a minterm is equal to the number of inputs in the Boolean function.

## 5. What is the significance of minterms and literals in a Boolean function?

Minterms and literals are important in simplifying and analyzing Boolean functions, as they can be used to create truth tables and logic circuits. They also play a crucial role in the process of converting a Boolean function into its canonical form.

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