Shifters and Leading Bit Counters

A shifter is a digital circuit that has two inputs and one output. It shifts one of the inputs by a number of bits defined by the second input. Although not strictly speaking arithmetic components themselves, shifters are pervasive in application-specific arithmetic. Their main use is to multiply by a power of two, to convert fixed-point to floating-point or the other way around, to align the binary representations of two numbers before adding them, and to normalize a floating-point result. In the latter case, the shift amount is the result of a leading bit count. This chapter covers all these use cases, studying their requirements and proposing relevant architectures.