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During the course of calculations using the (mantissa, exponent) representations, the exponents tend to become large and the mantissas small. This reduces the efficiency of computations using such representations significantly. The `normalisation' processes described here is extremely useful for avoiding such problems.

The name `normalisation' is used because this process is analogous to normalising a floating point number. This is slightly misleading, however, as a true normalisation process would normalise any representation of zero to a single unique representation. The process described here does not do that. As an aside, it would be possible to create an operation which modified each stream such that if it were zero the representation would be (say) an exponent of zero and a mantissa which was an infinite stream of the zero digits, but unfortunately we would not still not be able to test such a representation to determine if it actually represented the number zero (see section 2.2.2).


Martin Escardo