# Simplified Equivalent of Boolean Algebraic expressions

#### Hunter Neumann

Joined Aug 24, 2015
53
I am struggling learning how to simplify equations. If anyone can suggest a way to learn it that would be great. Right now I am just learning all of the different algebraic properties/identities and trying to apply them to simplify equations but its not clicking like I want it to. So if anyone has a special way they learned it or a way they like to think of it that works I would love to hear it. Thanks for your time

#### MrAl

Joined Jun 17, 2014
9,633
Hi,

Basically you really have to learn Boolean Algebra. It's like when you learn algebra and how to reduce or factor regular algebraic equations, except because of the limited and constrained domain of values available (0 or 1 only) there are more simplifications.
There are some tricks too you can try. One is to invert the equation and they try to simplify, then invert again and simplify again. This helps sometimes because the basic form of the expression changes when you invert it.
There are also different types of 'maps' that help. Certain patterns in the columns of the truth table mean certain things. But back when i worked in the industry i never used maps just Boolean Algebra and that always gave me what i wanted. I remember once i had to design a complex switching arrangement for a product that had to detect a lot of possible input states and act accordingly. Writing out the statements for each output and simplifying them using Boolean Algebra saved the day.
It takes a little getting used to, but once you do a few examples you start to see the beauty of the system as it usually reduces more than a regular algebra equation would, usually a lot more.

#### Hunter Neumann

Joined Aug 24, 2015
53
Hi,

Basically you really have to learn Boolean Algebra. It's like when you learn algebra and how to reduce or factor regular algebraic equations, except because of the limited and constrained domain of values available (0 or 1 only) there are more simplifications.
There are some tricks too you can try. One is to invert the equation and they try to simplify, then invert again and simplify again. This helps sometimes because the basic form of the expression changes when you invert it.
There are also different types of 'maps' that help. Certain patterns in the columns of the truth table mean certain things. But back when i worked in the industry i never used maps just Boolean Algebra and that always gave me what i wanted. I remember once i had to design a complex switching arrangement for a product that had to detect a lot of possible input states and act accordingly. Writing out the statements for each output and simplifying them using Boolean Algebra saved the day.
It takes a little getting used to, but once you do a few examples you start to see the beauty of the system as it usually reduces more than a regular algebra equation would, usually a lot more.
Thanks for the reply, all the informatics people in my class were outraged at having to learn this (it was funny to me) and he said all it takes is practice which I believe. I can tell that it will get easier once I familiarize myself with the basic concepts. Thanks for the suggestions as well

#### wayneh

Joined Sep 9, 2010
17,189
Just one word of practical experience: It's often helpful to have a goal in mind. For instance, in the real world, you might want to solve for a temperature, or a pressure, or an interval of time. Something tangible and you need either a number or an expression you can plug-n-chug to generate a table to plot out the function. It's so much easier in this case to keep working to an expression that is as simple as possible for your goal. Without that goal in mind, you can find yourself doing endless rearrangements that don't seem to accomplish anything.

Beyond that, you've probably already heard about the usual things. Separate variables, group like terms and so on. There are some clever tricks that can help but you won't remember them if you don't use them. Just learn that they exist, and where to look them up when you might need one.