Designing Embedded Hardware, 2nd Edition

Signed Numbers

Before getting into the nuts and bolts of assembly, let's take a quick look at how signed numbers are represented within the machine. Negative and positive numbers can be represented in binary (or hex) number systems by the state of the most significant bit. If the most significant bit is set, this indicates that the number is negative.

Tip

It is up to the programmer whether to treat the content of a register or memory location as signed or unsigned. In C, we are used to explicitly declaring a variable or pointer as either signed or unsigned. In assembly, it's up to you.

An 8-bit accumulator can have (in decimal) 0 to 255 (unsigned) or -128 to +127 (signed). Given a positive number, we use two's complement to convert this to its negative equivalent. Taking the two's complement of a number is done by inverting the bits (a one's compliment) and adding one to the result. So 0xFF is 1111 1111 (in binary) and is therefore negative. 0xFF is used to represent -1, 0xFE is -2, etc., all the way to 0x80, which is -128 (decimal).

For example, -3 as an 8-bit hex value is calculated in this way:

             0 0 0 0   0 0 1 1  (0x03)
Invert bits: 1 1 1 1   1 1 0 0  (0xFC)
Add 1 gives: 1 1 1 1   1 1 0 1  (0xFD)

So -3 is 0xFD in hex.

Note that we are not limited to using signed (positive and negative) numbers. We are free to ignore the sign bit and treat the byte as an unsigned number, giving us a range of 0x00 to 0xFF (255 decimal). It all depends on what we want the byte to represent.

16-bit, 32-bit, and ...