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.

We wish to construct a circuit that will form the sum of two 4-bit numbers. Let these numbers be A = = <A_{3} A_{2} A_{1} A_{0}> and T = = <T_{3} T_{2} T_{1} T_{0}> while the sum of A and T is S = = <S_{4} S_{0} S_{2} S_{1} S_{0}>.

The notation Y* _{i}* refers to bit

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