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Hi and welcome to the new lesson.

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Today we're going to talk about bits and.

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What they mean, bits are used to represent data, bits are grouped in bytes, eight bits form a byte.

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Bits are the smallest increment of data on a computer.

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They are usually referred to as either on and off.

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Which is very common, especially in an electrical engineering major or in the normal binary digit notation

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of one in zero.

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It's funny, but people say about other people that their binary if they can't really.

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Do anything in between things need either.

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All or nothing?

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Now the bigger picture bites.

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So eight bids can be grouped together to form KiloByte Megabyte Gigabyte Terabyte, and you can actually

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go ahead and deduce how many bids are in each one of these measuring units by multiplying the bytes

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by eight.

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Inbuilt significance, this is very important because you'll be using it a lot and.

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The bit that you have to them most right here, that is the least significant bit.

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And as it was, you go more to the left, the bits gained more significance.

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And this gets tied in with the next slide you're going to see in which you see the corresponding powers

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of two for each bit location inside a binary number.

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For example, this binary number one one one one one one one one has eight bits and the the least significant

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bit.

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It's tied to two to the power of zero.

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And as we move more to the left, this one gets tied in with the two to the power of one.

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And the third one with two to the power of two.

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And so on until we get to the last one, which gets tied in to with the two two, the power of seven.

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And this one, as you can see, holds more value, more decimal value in these than any of the other

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bits.

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So here this is probably where you'll visualize this more is because we get to actually calculate how

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to turn a binary number to decimal, so we have the same example one one one one one one one one.

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What you have to do is look in this table and say, OK, my number, this is my number here, starting

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from the least significant bit on the right.

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I say one times, two to the zero plus one times two to the one plus one times two to the two plus one

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times to the power three plus one times to the power of four plus one times to the power of five.

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And you can actually follow along here two plus one times two to the six.

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But this is where it came from.

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This table plus one times two to the power of seven.

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Now, if you actually perform the calculations, you will see that this number is equal to 255.

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And we'll take another example this time is the binary number one zero one zero one zero one one.

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And we'll do it the same way, so to find out the decimal value of this will have to.

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First, like, do the multiplication between this one and two to the zero, then add the multiplication

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between the.

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Bit here.

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And the two to the power of one plus zero times, two to the power of two plus one times three to the

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two to the power of three plus zero times two to the power of four plus one times to the power of five

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plus zero times to the power of six plus one times two to the power seven.

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And now we've performed the calculation and we find out that the number.

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In decimal base is 171.

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Normal notation for binary is a zero B in front of the number, but another use notations are the one

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that I have here on the bottom, where you just add a b at the end of the binary numbers c see here.

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We grouped this number into Nemours because it's easier to visualize for us humans, but in computer,

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in inside a computer like you won't have those spaces.

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And to turn a decimal number into binary, I like to start by dividing this number.

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I'll take this example number one.

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Thirty seven.

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And now divided to two.

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The result I'll market down here is sixty eight.

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And then I also take a note of my remainder.

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Very important.

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And then I take my result in nine divided by two.

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My result of that division is 34 and I have a remainder of zero.

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Now I divide thirty four by two and my result is 17.

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My remainder is zero.

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I divide 17 by two and my result is eight and my remainder is one.

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And I divide eight by two.

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My result is four and my remainder is zero.

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Now I have four divided by two.

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My result is two and my remainder is zero two, divided by two is one.

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And in this case, I'll just move the one over here.

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And this is what gives us the binary number from the most significant bit here to the least significant

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bit.

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So this is very important.

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You have to actually write down the result of this operation in this order.

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Top to bottom to top.

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So we would say one thirty seven in decimal is equal to be one zero zero zero.

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So from here, one zero zero one once again, I have separated my bits into nibbles just to make it

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easier to read.

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So if we want to turn this binary number one zero zero zero one zero zero one back to decimal, we know

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its value.

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It's one thirty seven.

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But how do we get to that value?

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Well, we have to use the table that I have presented in the previous slide.

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And you multiply each bit with the corresponding power in the and binary table and you add it with the

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next byte multiplied, but with its corresponding power of two and so on.

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We do with all the bits, and then we perform the calculations and we get a result of one thirty seven.

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So the next base we're going to talk about is Hexadecimal also called this base 16.

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It does use 16 characters to represent the bids.

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So these are numbers from zero to 15.

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Zero to nine is represented as we normally know it.

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But 10 to 15 are represented by the first six letters in the alphabet.

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So 10 is a 11 is B, 12, A C, 13 is D, 14 is E and 15 is F.

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And here I have the table of conversion for all the hexadecimal characters.

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Zero one two three.

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As you can see all the way to F.

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And you'll be using these to convert.

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All the hexadecimal expressions, too binary.

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That's very important.

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Now also, I want to point out that the known notation for hexadecimal is zero x, as you can see here,

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zero zero zero.

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You should use this to distinguish.

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A hexadecimal notation or no from another.

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Any other base like base 10 that doesn't have anything in front of it or binary or octal?

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OK, so now we're going to take concrete example and we're going to try to turn it into binary notation

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step by step.

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So we have X DeaDBeeF, the very popular cybersecurity example that everybody talks about or likes to

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use.

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So what we're going to do is we're going to go left to right and translate each one of these characters

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hexadecimal characters into their binary correspondence.

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But you can also start a right to left.

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It doesn't really matter as long as you keep translating them one by one and you put them in the position

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where they're supposed to be put the conversions like one after another.

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If you start left to right or you put the conversions like in front, if you start from right to left

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right, so you'll translate F and then you'll translate E and you'll put it right in front of the translation.

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For F, it's important to keep the order.

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So D will be b one one zero one e is or B one one one zero e is one zero one zero and so on.

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And now we have the final expression for dead beef in binary, and it's a very large number.

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So let's say now that we need to convert this number from binary to hexadecimal, and we have no idea

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what this would be like.

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It is very important to look from the least significant bit here.

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Towards the most significant bit here.

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And split it into nibbles.

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Right.

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Leave one space in between four bits, you always start from the least significant bit here.

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Group them into four.

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Right, so now this expression happens to be an exact number of nibbles, but sometimes you have like

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one left over here or two.

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And that's not an issue, just pad with extra zeros in front of them to create and nibble.

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If that is the case.

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So now, once you have it all split into Nemours, you can do the same thing.

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You either like start converting them one nibble at a time from the right to from the right to the left

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or from the left to the right.

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It doesn't matter if you already have them all separated into nibbles in the order that they're supposed

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to be.

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So one one zero one is the one one one zero is E and use the tables for this, as it's very common to

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just make a tiny mistake on one of these expressions thinking that, you know, then I do it all the

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time.

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One one one zero one one one zero one one is a one one zero one D. And so on.

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Now we have the full expression of that beef.

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So now let's talk about how to convert text to decimal.

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And remember, from binary, we were using the table of correspondence.

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So basically each one of these characters is used to represent a power of 16 because this is base 16.

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So as is representing the 16s to the zero that we have in this hexadecimal number E represents the sixteen

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to the power of ones that we have.

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E represent the 16s.

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Now, sixteen to the power of two and so on, so we're going to do exactly the same thing that we have

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done for the binary.

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Expressions.

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So we're going to go start here.

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The least significant character, and we're going to say f times 16 to the zero because you can see

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here plus e!

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Time 16 to the one.

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Plus, E times 16 to the second.

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Plus, B times 16 to the third and so on, you go and add all of these multiplications.

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And if you do the calculations, you'll see, you'll see that this is the number used to represent that

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beef in base.

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10.

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The very large number now remember that f e b, all of these letters are just used to represent the

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numbers, you know, 10 to 15.

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So each one has a correspondent.

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F is 15.

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That's why I do this here e is 14 and so on.

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The last base that I will touch base on today is octal, which is base eight.

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There are two notations that are not as utilized here, so either you put a zero in front of the actual

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number or you put a cue after the actual number.

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However, this one is the most popular.

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It's zero lowercase.

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Oh.

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So when base eight, you have eight characters, you have zero one, two, three, four, five, six

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and seven.

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And each one of these octal characters gets represented in binary by using three bits.

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So zero in octal would be binary zero zero zero one and octal would be binary zero zero one two in October

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will be binary zero one zero and so on.

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So this is something that you could keep handy if you are performing some actual conversions.

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So I'm going to take this example here six seven zero in October base eight and we're going to try to

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convert it to binary and the same as I did for hexadecimal works here, too.

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I just take each character.

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From my octal, no, and I turn it into its binary version.

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And I just write them in the same order.

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As they are in the actual number and and when I'm done with that, this here gives me my binary notation

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for the actual number six seven zero.

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So binary, that's one one zero one one one zero zero zero.

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And if you want to turn a binary number two actor, I recommend you start from the right and go to the

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left, grouping the bits three by three and then you perform.

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You convert each group of three bits into an actor character like you hear one one two zero is six one

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one one is seven and zero zero zero is eight.

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Is a zero sorry, so if you want to turn that an actual number to decimal?

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I took this ridiculously large number, but you you will use this table just like we did for binary

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and for hexadecimal.

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Each character in the actual number gets a power of eight.

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That corresponds to it.

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So keeping that in mind, the actual number two one three one zero four six zero and transformed into

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decimal would be seven times eight to the zero plus six times eight to the one plus four times eight

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to the second, plus zero times eight to the third plus one times aide to the power of four plus three

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times eight to the power of five plus one times eight to the power of six plus two times eight to the

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power of seven.

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So if we perform the calculations here, we see this octal number is equal to four million five hundred

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and fifty nine thousand one hundred fifty nine in base ten.

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And that was it for my lesson today.