Positional Numeral Systems - Hexadecimal, Octal, Duodecimal, Senary, Ternary Numeral System, Decimal Mark, Sexagesimal, Binary Numeral System (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 38. Chapters: Hexadecimal, Octal, Duodecimal, Senary, Ternary numeral system, Decimal mark, Sexagesimal, Binary numeral system, Vigesimal, Base64, Ascii85, Counting rods, Base 30, Base 36, Radix economy, Hexavigesimal, Nonary, Quinary, Base 24, Septenary, Quaternary numeral system, Base 13, Septemvigesimal, Pentadecimal, Undecimal, Base 32, Tetradecimal. Excerpt: The duodecimal system (also known as base-12 or dozenal) is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E' (another common notation, introduced by Sir Isaac Pitman, is to use a rotated '2' for ten and a reversed '3' for eleven). The number twelve (that is, the number written as '12' in the base ten numerical system) is instead written as '10' in duodecimal (meaning "1 dozen and 0 units," instead of "1 ten and 0 units"), whereas the digit string '12' means "1 dozen and 2 units" (i.e. the same number that in decimal is written as '14'). Similarly, in duodecimal '100' means "1 gross," '1000' means "1 great gross," and '0.1' means "1 twelfth" (instead of their decimal meanings "1 hundred," "1 thousand," and "1 tenth"). The number twelve, a highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range. As a result of this increased factorability of the radix and its divisibility by a wide range of the most elemental numbers (whereas ten has only two non-trivial factors: 2 and 5, with neither 3 nor 4), duodecimal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the duodecimal multiplication table. Of its factors, 2 and 3 are prime, which means the reciprocals of...