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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 UNSIGNED MODIFIER IN ACTION

The hardware rules for binary addition follow logical or mathematical principles: 0 + 0 = 0, 1 + 0 = 1, 0 + 1 = 1, and 1 + 1 = 10, which is referred to as a half adder in hardware. A full adder differs in that it has a carry input. You can modify the rules for the half adder to create a full adder (see Table 2).

The addition logic in a processor is built from full adder logic. For example, if you add the values 10 and 25 to it, you should get 35 as an answer.

0000 1010 (10) + 0001 1001 (25) = 0010 0011 (35)

But, what if you add numbers that overflow the 8-bit values? Letęs add 200 to 200, which equals:

1100 0100 (200) + 1100 0100 (200) = 1 1000 1000 (400)

Because you only have an 8-bit result, the carryover gets lost. Although the carry flag is set and could be checked for a problem, thatęs not usually done for every addition in a program.

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