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when you're asked to do 8-bit unsigned char conversions we already know that hex to binary to octal can be easily done here by just grouping also from BCD to decimal decimal to BCD again in grouping so the only real calculations we've seen before that we have to do is decimal to hex or hex to decimal and that relationship is shown in this line here so for instance if we want to go to 21 to 21 is over here and to 21 if we divide it by 16 the quotient is 13 which is d and the remainder is 13 which is d and so to 21 becomes DD now if we want a six a six is a little bit more on the side a six is a 10 times 16 plus six is 166 if we divide 16 and 166 that's ten with six remainders so it's very easy to convert across this entire line however when we start looking at 8-bit sign char things become a little bit more interesting notice any quills 1 here these numbers are positive n equals 0 or most significant bit is 0 positive as well however when we start dealing with a bit sign char n equals zero mean these are positive N equals 1 means that these are negative and you'll notice that if I have a number here like 5 a 5 a is 95 a here is 90 it's the same as before but if we have anything where the most significant bit is 1 like 8 9 ABCDEF is the first digit then we have a problem because this 82 FF is offset from this 82 FF by 256 or 2 to the 8th positions it's like we've snapped this off and slid it over here 256 positions so if I have a number up here which is 166 that I have here is definitely not going to be 166 it's a negative value so how do we work that out well it's very simple is 166 here over here is offset by 256 all we have to do is adjust that number by 256 so we start with 166 minus 256 that would give us our answer but if you're working this out by hand it's just as these a 256 subtract 166 write down your answer and remember to put a negative sign in and that's what we're going to have as the answer as you can see over here now to go back the other way if we have some negative number like minus 94 how do we go back the other way well we add 256 and then we convert across here and that two-digit number in hex will be the same as the one that we've got here and that's basically how are you going to do 8-bit sign char conversions now a couple gotchas here if it's the most significant bit is a 1 that means it's in this range which means you're going to have to figure it out here and convert this way and if it's not a 1 as you have in this case because 1 to 4 here will both 0 1 then it's in this range where you don't subtract it from 256 so you have to be a little bit careful with this but I think with a little bit of practice you should be able to get the hang of 8-bit sign char conversions