You might already be familiar with binary for example this is 1 1 is equivalent to 5 in decimal that's because this is the ones place this is the twos place fours place eights place 16 32 64 and 128 and we have a 1 in the fourth place and a 1 in the ones place 4 plus 1 is is 5 so this is fine but how might we represent a negative number so let's say we wanted to represent negative 5 well there's a couple ways we can do that one way is to take this 128 place and instead of using that as the 128 place use that as a sign so change this to a 1 here to indicate that this is negative and then the rest of it is the same 1 1 and so this would be 5 here and then instead of this representing 128 it represents that the number is negative so negative 5 now of course it's important to know how many bits you're working with right because if we're only using 4 bits then a 5 would be 1 1 that's equal to 5 but then we're going to use this this top bit here in this case we're only using 4 bits to the top that is this fourth bit and so negative 5 might be a 1 1 1 and now instead of this being the eights place this is actually representing a sign so this would be negative 5 and this would be 5 so it's important to know how many bits you're working with so that you know which bit is the first bit and therefore which bit indicates what the sign of the number is so to keep going with this example we can look...

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