# Engineering Math Software and Boolean Algebra

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Am I thinking Boolean? This is a question that I’ve asked myself a couple of times. To put it simply, a Boolean expression is an expression whose result is either true or false, and this type of expression is defined using logical operators that help us evaluate such expressions. We are logical beings that have to make decisions at every turn, and sometimes we even have to respect some boundaries. I’d like to think that I’m not, but my engineering math software, PTC Mathcad, does think Boolean.

To define such expressions using PTC Mathcad, we need to know what operators are available. Let’s make things easier by splitting them into two categories:

• Comparison operators (=  ≠  <  ≤  >  ≥) are used to compare valid math expressions.
• Logical operators () treat any numerical value which is not zero as true, including complex numbers.

So how we can use this to solve daily problems? Here are two examples.

## Booleans Inside Engineering Math Software Solve Blocks

You can use the Boolean operators inside a Solve Block to set the boundary conditions (constraints). Let’s say that we want to determine the minimum dimensions for the cross section of a rectangular beam so that the moment of inertia is not greater than 10,000 cm4 and the width is at least 5 times smaller than the height.

In Mathcad this translates to the following:

As you can see in the image above I’ve put to good use the Comparison operators so that the results match my requirements. What you must know is that apart from ≠, you can use any of the operators for specifying constraints in solve blocks.

## Booleans to Analyze Logical Circuits

You can also analyze logical circuits in Mathcad using Boolean expressions. Any circuit, no matter how complex it may be, can be described using Boolean operations. That’s because the logical gates OR, AND, and NOT are the building blocks of the digital systems. For example, consider the circuit below that has 3 inputs and one output. The expression for x is determined very easily using the Boolean expressions for each logical gate.

Then I can also evaluate the logical level of the output by setting the logical values for the inputs as you can see below:

Boolean operators can also be used when defining functions that use the programming functions or when performing looping procedures.

Bottom line: Boolean expressions can be used for various types of problems and Mathcad provides the tools to solve them.

[Ed.The mathematical calculation software you select should support the specific math you do and allow you to centralize all engineering knowledge and design intent. Download our checklist "Choosing Mathematical Calculation Software" for the six decisions you should make when choosing software.]