From the course: CompTIA Tech+ (FC0-U71) Cert Prep

Basics of binary

From the course: CompTIA Tech+ (FC0-U71) Cert Prep

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Basics of binary

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- How many fingers am I holding up? 10, right? This is how humans count. It's called base 10. We count things from zero to nine and then it goes to 10 and beyond. Computing devices don't work that way. Computing devices use wires and electricity. They use a math called binary, or base two. It's all about the state of electricity on a wire. If a wire has electricity on it, it's on, right? We call that a one. If it doesn't have electricity, it's off. We call that a zero. Let's take a look at the way we can use binary and talk about binary math so that it's totally relevant for computing fundamentals. I have here a circuit board connected to a battery pack and two little LED circuits. Now, when I make a connection to one of these circuits, like this guy here on the left, the LED turns on, and when I take it away, it turns off. So you can say that the state of the connection, right, is either on or off. In binary, we use the terms one or zero. So on is one, off is zero. Now with two LEDs, I double the number of combinations, right? So for example, these two circuits can both be off like they are here, zero, zero. They can be on, off, one, zero. Off, on, zero, one. Or on, on, one, one. Got it? Every wire we add doubles the number of combinations. So for a single wire, you have two states, right? It can either be on or it can be off. With two wires, that number doubles. It can be up to four different combinations of on or off. With three wires, six? No. Right, it doubles. Eight different combinations. And so on from there. Four wires, 16, 32, 64, 128. Get it? Modern central processing units come in a couple of different varieties, 32 bit and 64 bit. Modern operating systems also come in 32 bit and 64 bit to take advantage of the more complex CPUs. A 32 bit CPU with a 32 bit operating system can only handle up to four gigabytes of ram. That means the number of possibilities of on or off, right, are 4,294,967,296. When I go from 32 bit to 64 bit, does that double the number of combinations? Come on, yes or no? 50/50? No, of course not, right? Just going from 32 bit to 33 bit would double the number of possibilities. Instead, going from 32 bit to 64 bit makes this gigantic jump. And how that's absolutely important in computing is in the amount of RAM that the CPU with the operating system can handle. So a 64 bit CPU with a 64 bit operating system can handle way more than four gigabytes of ram.

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