Arithmetic and Logic

Abstract

So far we have seen how to represent numbers as binary vectors and how, using transistors, one can implement logic gates that perform the basic Boolean operations NOT, AND, and OR. In order to realise the goal of performing useful computation on integer values represented as $n$-bit vectors, we need to compose these logic gates into higher-level circuits. Generally speaking, the Arithmetic and Logic Unit (ALU) packages circuits for different operations into one component that performs computation for the processor. To aid the discussion in examples we set $n=8$ throughout, i.e., set the size of a word to equal one byte. However, it is important to see that the methods are presented in a general form: one can easily extend them to cope with larger word sizes.