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NUMBER CRUNCHING WITH EMBEDDED PROCESSORS

by George Martin

Start ę The Unsigned Modifier in Action ę The Signed Notation ę A Lesson in Subtraction ę Sources and PDF

THE SIGNED NOTATION

If you want to work with negative numbers, you need another notation called twoęs complement notation. Table 3 illustrates the notation needed for an 8-bit register.

This notation is called signed in C, and itęs the default mode if you donęt use a modifier. And, because the hardware doesnęt know the difference, the binary addition still takes place. The notation is just that, a notation. It gives something the programmer can use.

Note that this twoęs complement notation is linear. With addition, each larger value is a result of adding one to the smaller value, and for subtraction, the converse is true. In fact, the computeręs hardware uses twoęs complement notation when performing subtraction. The subtrahend is converted to twoęs complement and then added to the minuend.

To convert a number to its negative, invert all the bits and add one (see Table 4). Look back at Table 3 and do the twoęs complement conversions. Isnęt zero interesting?

Twoęs complement notation forms the basis of signed and unsigned notation. Simply tell the compiler which representation the variable will take so the compiler can generate the proper assembly language instructions, but the CPU does not change its operation.

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