Numerical Systems
An ALU must process numbers using the same format as the rest of the digital circuit. The format of modern processors is almost always the two's complement binary number representation. Early computers used a wide variety of number systems, including Ones' complement, Two's complement, sign-magnitude format, and even true decimal systems, with various representation of the digits. ALUs for each one of these that makes it easier for the ALUs to calculate additions and subtractions.
The ones' complement and two's complement number systems allow for subtraction to be accomplished by adding the negative of a number in a very simple way which negates the need for specialized circuits to do subtraction; however, calculating the negative in two's complement requires adding a one to the low order bit and propagating the carry. An alternative way to do two's complement subtraction of A−B is to present a one to the carry input of the adder and use ¬B rather than B as the second input. The arithmetic, logic and shift circuits introduced in previous sections can be combined into one ALU with common selection.
Read more about this topic: Arithmetic Logic Unit
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