Fundamentals of Data representation

The set of positive integers and 0. They can be used as cardinal(counting) or ordinal(ordering) numbers. N = {0, 1, 2, 3, …}.

The set of numbers with no fractional part. The natural numbers are a subset of the integers. {…, -3, -2, -1, 0, 1, 2, 3, …}.

The set of numbers that can be expressed as the ratio of two integers. The integers are a subset of the rational numbers since all integers can be expressed as a ratio with 1. Q = {0, 1/2, 0.75, 0.11111…, 300.5, -42, …}.

Numbers which cannot be expressed as a ratio of two integers, and hence do not lie within the set of rational numbers. {π , √2, e, …}.

The set of numbers that can represent real world quantities and have an imaginary part of 0. Rational and irrational numbers are all members of the real numbers. R = {π , 1.5, -7, 3/4, 2, 10000000, -11.3432, …}.

Natural numbers used to describe numerical position or order of objects.

A number system that only uses ones and zeros to represent numbers (a base 2 system).

A number system that only uses 10 characters (0 to 9) to represent numbers 9a base 10 system).

A number system that only uses 16 characters (0 to 9 and A to F) to represent numbers (a base 16 system).

The number of unique digits used by a particular number system to represent numbers.

A binary digit used by computers as the fundamental unit of information.

A group of 8 bites.

A prefix to a unit representing a power of 2. (Kibi=2^10, mebi=2^20, gibi=2^30, tebi=2^40).

A prefix to a unite representing a power of 10. (Kilo=10^3, mega=10^6, giga=10^9, tera=10^12).

A binary number system that can represent both positive and negative numbers.

A binary number system that can only represent positive numbers.

A coding scheme used in signed binary to represent negative as well as positive numbers. A negative number is represented by flipping all its digits and adding 1 to the most significant bit.

A component of floating point form that stores the number of positions to move the decimal point.

A form used to represent numbers with a fractional part in any number system. Digits after the fixed point are multiplied by the base raised to a negative power.

A component of floating point form that stores the non-zero significant digits of a number.

Errors inherently introduced to any calculations with fixed or floating point numbers since they cannot store numbers with infinite precisions.

The difference between the exact correct value and rounded value.

The percentage difference between the exact correct value and rounded value.

The process of ensuring a float point number is represented as efficiently as possible by adjusting the position of the radix point and exponent.