Number Systems and Bases

• ℕ is the set of all natural numbers, containing all positive integers
• ℤ is the set of all integer numbers, containing all integers, both positive and negative
• "..." is used to indicate the set continues in an obvious way infinitely
• ℚ is the set of all rational numbers, containing all numbers that can be represented as a fraction or ratio
• ℝ is the set of all real numbers, containing all possible real world values
• Ordinal numbers describe the numerical position of an item
• An irrational number cannot be represented as a fraction, for example pi
• Denary, or base 10, is the number system used by people across the world, ranging from 0 - 9
• Binary, or base 2, is the number system used in computing, ranging from 0 - 1
• Hexadecimal, or base 16, is useful to represent large numbers, ranging from 0 - 15, where A = 10 and F = 15
• Hexadecimal can be used as shorthand for binary which is easier to read
• The smallest unit of information in computing is a bit, which is either a 1 or a 0
• A byte consists of 8 bits
• For n number of bits, there are 2^n possible values that can be stored in them
• Quantities of bytes can be described with binary prefixes representing powers of 2, or denary prefixes representing powers of 10
• Kibibyte or KiB represents 2^10 (1024) bytes
• Mebibyte or MiB represents 2^20 bytes or 1024 kibibytes
• Gibibyte or GiB represents 2^30 bytes or 1024 mebibytes
• Tebibyte or TiB represents 2^40 bytes or 1024 gibibytes
• Kilobyte or KB represents 10^3 (1000) bytes
• Megabyte or MB represents 10^6 bytes or 1000 kilobytes
• Gigabyte or GB represents 10^9 bytes or 1000 megabytes
• Terabyte or TB represents 10^12 bytes or 1000 gigabytes
• Natural numbers are helpful for counting, while real numbers are good for measurement
• A number base can be represented as a smaller number at the bottom to the right of a number (similar to exponents, this is a subscript)