Type Signed Made Easy

Type signed

all right so in this lesson we're going to talk about signed and unsigned numbers now very briefly a signed number means a number that can be positive or negative and an unsigned number means a number that can only be positive now this lesson applies to all programming languages not just C now we've already discussed that computers represent all data as binary we also discussed that it is impossible to distinguish one datatype from another just by looking at it because any given sequence of binary could be part of absolutely anything may be a number or text or part of a movie or anything at all even a program for this lesson we are going to only discuss numbers now let's examine the following binary number now this number is of course 7 if I asked you to store that inside of your computer what is the minimum size that you require the answer is 3 bits each bit in your computer is effectively a single one or zero and three of those bits will be big enough to store any value from 0 through 7 all right but what happens if you need to store the number 8 well you can't do that with only 3 bits you need at least 4 bits because 8 is represented using 4 binary digits and since 8 is represented using 4 binary digits you need at least 4 bits in order to store the number 8 if you needed to store a number 16 or greater you need at least 5 bits so here we learn two very important principles first of all you can see that the number of bits determines the maximum size of any number so if you only have 3 bits you can't store a value greater than 7 and so on secondly you see that just by adding one bit to the end of any binary sequence effectively doubles its capacity so whereas with 3 bits you can store 8 different values that's 0 through 7 with 4 bits you can store 16 different values 0 through 15 and every time you add a bit you double how much can be stored so I want to explore this a bit more so that you can understand something about binary at a fundamental level let's look at a sample table of binary numbers now we start at 0 and we go all the way to 7 now if we start at 8 and continue we have a second table that you see to the right and finally at 15 were done so between 0 and 15 we have stored a total of 16 different values now did you notice that we simply repeated the first table of 0 through 7 a second time but with a 1 in front of it whereas over here we have a 0 in front this is because the one on the far left over here effectively means add eight so any number over here if we change the zero to a one we add eight we could also do something else here if we wanted to we could choose to say that both sequences are counting from zero to seven except we could say that the far left digit right here is a flag indicating if we want the number to be positive or negative we could choose to say that instead of an eighth place this fourth column from right to left means positive or negative we could say then that if it's set to a zero it means positive and if it's set to a 1 it means negative whenever you encode a number in binary in such a way that it can be either a positive or a negative number that is known as a signed number this specific method that I am introducing is known as signed magnitude it basically means that the furthest digit over to the left is a flag indicating whether or not the number is positive or negative so for example this is positive 3 and this is negative 3 whenever you define a bit as a flag for stating if a number is positive or negative that bit is called the sign bit in this case a sign bit of zero means positive number and a sign bit of one means negative number now here you should notice something important when you are using four bits if this were an unsigned number we could count all the values from 0 to 15 however when we make the eights place into a flag for positive or negative numbers we can only now count half as much as before but we can do so in two different directions so we can count from zero to seven and then we can count from either we can say from eight to 15 or we can say from zero to negative seven now remember that this is a system we are just using for the purpose of this lesson I'm not saying that this is the best way to represent positive and negative numbers in fact you immediately notice a problem which is that we're effectively saying 0 twice which seems that we are not doing things as efficiently as we could but we'll get into that in a later lesson I want you to understand the concept of using a sign bit to indicate a positive or a negative number so I want you to get three things out of this lesson okay so first of all you learned that you can specify a number as being negative or positive using a sign bit and a sign bit is simply a binary place value that rather than having a numeric value like say the eights place it is rather an indicator of whether or not the number is positive or negative secondly when you have a sign bit you can only count half as far but you can do so in two directions positive and negative and last the same exact binary can encode a signed number or an unsigned number for example the binary sequence 1 0 1 0 could mean 10 or it could mean negative to keep in mind it is up to you the programmer to specify how any given binary sequence is going to be interpreted you might be asking yourself ok so how do i how do I know whether it is a signed number or an unsigned number and I'll show you exactly how to do that in later lessons but I want you to get a feel for the idea that you get to decide these things as the programmer you might come up with a totally different method of storing values in binary and you might decide that a given place value is numeric another place value is a flag for some purpose but the point is you get to decide these details so in this lesson I've introduced you to signed and unsigned numbers and I've shown you one method of using binary sequences along with a sign bit in order to represent signed numbers and unsigned numbers we'll explore this more in later lessons but I want you to remember that a signed number is a number that can be positive or negative and in order to be positive or negative there has to be a flag a sign bit which can be set to one or zero to indicate whether the number is positive or negative and secondly an unsigned number has no sign bit and rather every binary digit has a numeric value which means that you are limited only to positive numbers