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4

Computer arithmetic

A result of our choosing to represent numbers in binary notation is that we can devise logic circuits to process the numbers. In this chapter, we design a simple adder circuit and develop it into a more useful ALU (arithmetic and logic unit). We see how the simple adder can be made to operate faster by using the carry-look-ahead technique. Finally, we look at how floating-point numbers are represented and how arithmetic is performed on them.

## 4.1 Circuit to add numbers

We wish to construct a circuit that will form the sum of two 4-bit numbers. Let these numbers be A = = <A3 A2 A1 A0> and T = = <T3 T2 T1 T0> while the sum of A and T is S = = <S4 S0 S2 S1 S0>.

The notation Yi refers to bit i of number Y. As noted in Chapter ...

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