Signed versus Unsigned Integers

Question

Unsigned can hold a larger positive value and no negative value.

Yes.

Unsigned uses the leading bit as a part of the value, while the signed version uses the left-most-bit to identify if the number is positive or negative.

There are different ways of representing signed integers. The easiest to visualise is to use the leftmost bit as a flag (sign and magnitude), but more common is two's complement. Both are in use in most modern microprocessors — floating point uses sign and magnitude, while integer arithmetic uses two's complement.

Signed integers can hold both positive and negative numbers.

Yes.

I'll go into differences at the hardware level, on x86. This is mostly irrelevant unless you're writing a compiler or using assembly language. But it's nice to know.

Firstly, x86 has native support for the two's complement representation of signed numbers. You can use other representations but this would require more instructions and generally be a waste of processor time.

What do I mean by "native support"? Basically I mean that there are a set of instructions you use for unsigned numbers and another set that you use for signed numbers. Unsigned numbers can sit in the same registers as signed numbers, and indeed you can mix signed and unsigned instructions without worrying the processor. It's up to the compiler (or assembly programmer) to keep track of whether a number is signed or not, and use the appropriate instructions.

Firstly, two's complement numbers have the property that addition and subtraction is just the same as for unsigned numbers. It makes no difference whether the numbers are positive or negative. (So you just go ahead and ADD and SUB your numbers without a worry.)

The differences start to show when it comes to comparisons. x86 has a simple way of differentiating them: above/below indicates an unsigned comparison and greater/less than indicates a signed comparison. (E.g. JAE means "Jump if above or equal" and is unsigned.)

There are also two sets of multiplication and division instructions to deal with signed and unsigned integers.

Lastly: if you want to check for, say, overflow, you would do it differently for signed and for unsigned numbers.

He only asked about signed and unsigned. Don't know why people are adding extra stuff in this. Let me tell you the answer.

1. Unsigned: It consists of only non-negative values i.e 0 to 255.

2. Signed: It consist of both negative and positive values but in different formats like

   • 0 to +127
   • -1 to -128

And this explanation is about the 8-bit number system.

According to what we learned in class, signed integers can represent both positive and negative numbers, while unsigned integers are only non-negative.

For example, looking at an 8-bit number:

unsigned values 0 to 255

signed values range from -128 to 127

Just a few points for completeness:

• this answer is discussing only integer representations. There may be other answers for floating point;

• the representation of a negative number can vary. The most common (by far - it's nearly universal today) in use today is two's complement. Other representations include one's complement (quite rare) and signed magnitude (vanishingly rare - probably only used on museum pieces) which is simply using the high bit as a sign indicator with the remain bits representing the absolute value of the number.

• When using two's complement, the variable can represent a larger range (by one) of negative numbers than positive numbers. This is because zero is included in the 'positive' numbers (since the sign bit is not set for zero), but not the negative numbers. This means that the absolute value of the smallest negative number cannot be represented.

• when using one's complement or signed magnitude you can have zero represented as either a positive or negative number (which is one of a couple of reasons these representations aren't typically used).

Everything except for point 2 is correct. There are many different notations for signed ints, some implementations use the first, others use the last and yet others use something completely different. That all depends on the platform you're working with.