Chapter 1. Introduction
10
10 digit string can represent a value up to 10 digits worth of accuracy. I.e. the
number 1/3 would be equal to 0.3333333333.
• A signed string of digits that represent the exponent, that modifies the magnitude
of the number. The length of the string represents the range of the numbers that
can be represented.
• An unsigned number which represents the base which is usually the number 2.
To derive the value of the floating-point number, one must multiply the significand by
the base raised to the power of the exponent, equivalent to shifting the radix point from
its implied position by a number of places equal to the value of the exponent to the right
if the exponent is positive or to the left if the exponent is negative.
1.4.3
The IEEE 754 standard
The most used floating point format used today is the IEEE 754. The IEEE has stan-
dardized the representation used in most today’s computers with some exceptions. The
technical standard was established in 1985 and defines the following:
• arithmetic formats: sets of binary and decimal floating-point data, which consist
of finite numbers (including signed zeros and subnormal numbers), infinities, and
special ”not a number” values (NaNs)
• interchange formats: encodings (bit strings) that may be used to exchange floating-
point data in an efficient and compact form
• rounding rules: properties to be satisfied when rounding numbers during arith-
metic and conversions
• operations: arithmetic and other operations on arithmetic formats
• exception handling: indications of exceptional conditions (such as division by zero,
overflow, etc.)