- In the last episode, discussed how computers evolved from "electromechanical devices," which often had decimal representations of numbers like those represented by teeth on a gear, to "electronic computers" with transistors t

hat can turn the flow of electricity on or off. 

- The fortunate part of two states of electricity was we could represent crucial information, which is called Binary. 

- In computers, an "on" state, when electricity is flowing, represents true. The "off" state, no electricity flowing, represents false. We can also write binary as 1's and 0's instead of true's and false's, just different expressions of the same signal. 

- Some early electronic computers were ternary, that's three states, and even quinary, using five states. So why they happened? 

- The problem of ternary or quinary computers is, the more intermediate states there are, the harder it's to keep them all seperate. If your smartphone battery starts running low or there's electrical noise because someone's running a microwave nearby, the signals can get mixed up. This problem only gets worse with transistors changing states millions of times per second. So using two signals as far apart as possible - using just 'on and off' - gives us the most distinct signal to minimize these issues. 

- Another reason computers use binary is that an entire branch of mathematics already existed that dealt exclusively with true and false values. And it had figured out all of the necessary rules and operations for manipulating them. It's called Boolean Algebra. George Boole, from which Boolean Alebra later got its name, was a self-taught English mathematician in the 1800s. 

- In regular algebra -- the type you probably learned in high school -- the values of variables are numbers, and operations on those numbers are things like addition and multiplication. But in Boolean Algebra, the values of variables are true and false, and the operations are logical. There are three fundamental operations in Boolean Algebra: a NOT, an AND, and an OR operation. 

- Also, XOR, Exclusive OR, is critical. If input A is true and input B is also true, the output is false.