# Can someone simplified this boolean

• tonyzgolfer
In summary, a boolean is a data type in computer programming with two values: true or false, commonly used in conditional statements. Simplifying a boolean can make code easier to read and more efficient, and can be done using logical operators or truth tables. Common mistakes include using the wrong operator and not considering all possible scenarios. An example of simplifying a boolean is simplifying (x > 5 && y < 10) to (x > 5).
tonyzgolfer

## Homework Statement

here are my function.

s = xy'z + x'y'z + xyz

boolean algebra

## The Attempt at a Solution

after i try many boolean law. i got this
c. F(x,y,z) = xy’z+x’y’z+xyz
= xy’z + x’y’z + x’y’z + xyz
= y’z(x + x’) + x’y’z + xyz
= y’z(x + x’) + z(x’y’+xy)
= y’z(1) + z(x’y’+xy)
but i stuck in this line
i know x'y'+xy is (x xor y )'

what is the simplest ?

tonyzgolfer said:

## Homework Statement

here are my function.

s = xy'z + x'y'z + xyz

boolean algebra

## The Attempt at a Solution

after i try many boolean law. i got this
c. F(x,y,z) = xy’z+x’y’z+xyz
= xy’z + x’y’z + x’y’z + xyz
= y’z(x + x’) + x’y’z + xyz
= y’z(x + x’) + z(x’y’+xy)
= y’z(1) + z(x’y’+xy)
but i stuck in this line
i know x'y'+xy is (x xor y )'

what is the simplest ?

First, you have two terms in the initial equation that have y'z in them. You have them correctly combined in your last equation above.

Second, if you use a Karnaugh map to help you see what to do in the logic, that may help. Draw a K-map of the 3 terms in the equation. See how the y'z combination becomes obvious? Do you see another combination that will get you to the minimim implementation?

Without using a Karnaugh map:

F(x,y,z) = xy'z + x'y'z + xyz
= (xy'z + x'y'z) + xyz
<< middle steps edited out by berkeman >>
= (y' + x)z
= y'z + xz

zgozvrm said:
Without using a Karnaugh map:

F(x,y,z) = xy'z + x'y'z + xyz
= (xy'z + x'y'z) + xyz
<< middle steps edited out by berkeman >>
= (y' + x)z
= y'z + xz

Please do not do all the work for the OP. They must be doing the bulk of the work on their homework/coursework problems.

I always prefer to use Karnaugh maps with these sort of problems since I'm more visual, so give that a try.
Otherwise, zgozvrm has posted a useful start. I'd continue using De Morgan's law.

I, too, prefer using Karnaugh maps for this sort of problem. I was simply showing how to solve the problem using Boolean algebra, since the OP was going that route. Perhaps, the original problem stated that Boolean algebra was required, or that Karnaugh maps were not to be used.

## 1. What is a boolean?

A boolean is a data type in computer programming that can only have two values: true or false. It is often used in conditional statements to determine the flow of a program.

## 2. Why would someone want to simplify a boolean?

Simplifying a boolean can make code easier to read and understand, as well as make it more efficient. It can also help to avoid potential errors or bugs in the code.

## 3. How can someone simplify a boolean?

There are a few different ways to simplify a boolean, including using logical operators (such as AND, OR, and NOT) and using truth tables. It ultimately depends on the specific context and purpose of the boolean in question.

## 4. What are some common mistakes when simplifying a boolean?

One common mistake is using the wrong logical operator, which can change the outcome of the boolean. Another mistake is not considering all possible scenarios and simplifying based on incomplete information.

## 5. Can someone provide an example of simplifying a boolean?

Sure, for example, if we have a boolean expression like (x > 5 && y < 10), we can simplify it to (x > 5) since the second condition (y < 10) is already implied by the first one. This results in a more concise and easy to understand boolean expression.

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