By Yan S.Y.
This booklet offers an easy creation to formal languages and computer computation. The fabrics coated contain computation-oriented arithmetic, finite automata and normal languages, push-down automata and context-free languages, Turing machines and recursively enumerable languages, and computability and complexity. As integers are vital in arithmetic and desktop technology, the booklet additionally features a bankruptcy on number-theoretic computation. The e-book is meant for collage computing and arithmetic scholars and computing execs
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Additional info for An Introduction to Formal Languages and Machine Computation
This is the approach taken by the IEEE standard, to be discussed in the next chapter. In either case, there is the question of what to do about the sign of zero. Traditionally, this was ignored, but we shall see a different approach in the next chapter. The Toy Number System It is quite instructive to suppose that the computer word size is much smaller than 32 bits and work out in detail what all the possible floating point numbers are in such a case. Suppose that all numbers have the form with 60 stored explicitly and all nonzero numbers required to be normalized.
Chapter 5 Rounding We saw in the previous chapter that the finite IEEE floating point numbers can all be expressed in the form where p is the precision of the floating point system with, for normalized numbers, bo = 1 and Emin < E < Emax and, for subnormal numbers and zero, 60 = 0 and E = £-min- We denoted the largest normalized number by Nmax and the smallest positive normalized number by N min . There are also two infinite floating point numbers, ±00. We now introduce a new definition. We say that a real number x is in the normalized range of the floating point system if The numbers ±0 and ±00 and the subnormal numbers are not in the normalized range of the floating point system, although they are all valid floating point numbers.
0, since the bit 60 is hidden. There are two ways to address this difficulty. The first, which was used by most floating point implementations until about 1975, is to give up the idea of a hidden bit and instead insist that the leading bit 60 in the binary representation of a nonzero number must be stored explicitly, even though it is always 1. In this way, the number zero can be represented by a significand that has all zero bits. This approach effectively reduces the precision of the system by one bit, because, to make room for 60> we must give up storing the final bit (623 in the system described above).
An Introduction to Formal Languages and Machine Computation by Yan S.Y.