In computing, a normal number is a non-zero number in a floating-point representation which is within the balanced range supported by a given floating-point format.
The magnitude of the smallest normal number in a format is given by bemin, where b is the base (radix) of the format (usually 2 or 10) and emin depends on the size and layout of the format.
Similarly, the magnitude of the largest normal number in a format is given by
bemax × (b − b1−p),
where p is the precision of the format in digits and emax is (−emin)+1.
In the IEEE 754 binary and proposed decimal formats, p, emin, and emax have the following values:
Format
p
emin
emax
binary 32-bit
24
−126
127
binary 64-bit
53
−1022
1023
binary 128-bit
113
−16382
16383
decimal 32-bit
7
−95
96
decimal 64-bit
16
−383
384
decimal 128-bit
34
−6143
6144
For example, in the smallest decimal format, the range of positive normal numbers is 10−95 through 9.999999 × 1096.
Non-zero numbers smaller in magnitude than the smallest normal number are called denormalized numbers or subnormal numbers. Zero is neither normal nor subnormal.
No rational number is normal to any base, since the digit sequences of rational numbers are eventually periodic.
A computablenormalnumber was constructed by VerĂ³nica Becher and Santiago Figueira; an example of an uncomputable normalnumber is given by Chaitin's constant
It is extremely hard to prove the normality of numbers which were not explicitly constructed for the purpose.
Interactive computer simulations based on this strategy help students to create explanations for the events and argue for the validity of those explanations using a mixture of their own ideas and technical concepts in the simulation.
Computer simulations were found to be very effective in stimulating environmental problem solving by community college students (Faryniarz and Lockwood, 1992).
In particular, computer simulation exercises based on the guided discovery learning theory can be designed to provide motivation, expose misconceptions and areas of knowledge deficiency, integrate information, and enhance transfer of learning (Mayes, 1992).
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