My Own Personal Yellow Brick Road
Another Slight Detour… into Boolean Algebra
Categories: Explorations

One thing that has kept coming up in my research has been the term Boolean algebra or Boolean logic, this apparently is a system of logic that was developed in the 1840′s by a chap called George Boole. It basically laid out several rules of relationships between mathematical quantities that were limited to being true or false, 1 or 0 (this is starting to look familiar…).Since then some clever bod at MIT realised that Boolean algebra could be applied to looking at digital circuits, what with all those 1s and 0s. Boolean algebra is a powerful too for designing and analysing digital circuits, it can show where systems can be simplified, Ive pasted in below a couple of slides I found from a powerpoint on the subject﻿﻿:

You take a Boolean expression of a logic circuit (the bars over some of the outputs mean that they are inverted)…

Simplify it using regular algebraic rules and Boolean logic rules…

And convert the result back into a logic circuit…

This subject is huge and requires going much deeper into the subject than I have need for in this project but I found this site a great resource when I was trying to understand the basics: http://www.allaboutcircuits.com/vol_4/chpt_7/1.html

It’s amazing that a system of logic developed in the 1800′s could have such a huge significance in developing cutting edge technology today.