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Well welcome back this is the appendix on the hexadecimal number system first of all let's talk about why we would need to use yet another number system the hexadecimal number system humans would have been using the decimal number system for a long long time and now we have computers that use the binary number system one more number system and it's used to help us represent the numbers that are internally represented as binary so if you look at this binary number with all these ones and zeros this is not something that you would want to write down and try and figure out what this means you wouldn't call someone up and read this number to them on the phone they couldn't possibly write it down so we need a more human way of representing these binary numbers and it'll come clear to you why we've chosen the hexadecimal number system because of the conversion between binary and hexadecimal so the computers are working in binary and we need an easier way to look at these binary numbers a more human way that's why we've chosen the hexadecimal number system well hexadecimal or sometimes we'll just call this hex is base 16 in the previous pendeks we compared base 10 the decimal number system that we've been using all our lives and base 2 or the binary number system in base 16 or the hex number system we have 16 symbols to work with similarly in decimal we had 10 symbols and in base 2 we had 2 symbols so there aren't 16 different digits that we can use as symbols in the in the hex number system so we borrowed letters and we're going to use the letters A through F to represent the values 10 through 15 so the hex number system base 16 uses these 16 symbols 0 through F and a good way to start working in hex and getting a feel for it is to just go to a spreadsheet and start to count in hex and count along with the other decimal the other number systems decimal and binary so let's go do that now one of the best ways to get started thinking about hexadecimal is to just look at some numbers as we count in the different number systems so here is in the third column counting in decimal which is what we've been doing since we were children 0 through 15 and if we compare that to counting in binary 0 is the same in all number systems and then in binary 1 is the same in all number systems actually and then in binary to represent 2 you need to have 2 places 1 0 and so on when we reach 10 something different happens in hex we still want to represent 10 in 1 hex place but we don't have a symbol for that so we introduce letters as well so in hexadecimal the character a the symbol a is going to represent 10 and so on up until F is going to represent the value 15 so when we go to 16 in binary we need one more place so we would say 1 0 0 0 0 we have 5 binary places now to represent 16 in decimal of course 16 is 16 and in hex we have one group of 16 and 0 groups of 1 so how would we represent 17 in decimal it's 17 in binary one group of 16 and one group of 1 and in hex one group of 16 and one group of 1 so here's what's happened in hex we have 16 different symbols because it's base 16 and we've added the symbols a through F the reason that we use hex is because for binary places translate into 1 hex place so it isn't a coincidence that 1 1 1 1 is the largest value we can represent in 4 bits and that's also the largest value we can represent in one hex place which is the character F ok as we continue to look at the hexadecimal number system or base 16 let's go back and review the base 10 and base 2 so in base 10 we started out by looking at a regular decimal number 983 and we explored that that's the same as 9 times 10 to the power of 2 or nine hundreds 8 times 10 to the 1 or eat tens eighty and three times 10 to the zero or three ones so 983 this is the number system that we're used to using all our lives nine hundred and eighty three is nine hundreds eight tens and three ones in binary which is base 2 we had an example number 1 1 0 1 we looked at what that meant the first one the most significant one is 1 times 2 to the power of 3 2 cubed is 8 so one group of eight one group of for one group of two no sorry zero groups of two and one group of one so if we add these up one one zero one in binary turned out to be the equivalent in decimal of the number 13 in hexadecimal or base 13 we're going base 16 we're going to use our powers of 16 to determine the value of the places so 16 to the 0 is 1 16 to the 1 is 16 16 squared is 256 and 16 cubed is 4096 so we have a ones place as we have in all number systems a 16s place at 256 is place and up 4096 is place these get very large very fast in base 16 so have a look at this example number in hex 3f 8 let's explore what that means when you write a number in hex we typically will write 0x at the first of it so that we can tell that

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