# Numeration Systems

## Modulo-m Systems

If m is an integer greater than 1, then a modulo-m system consists of the numbers 0,1,2,…,m−1. Counting and arithmetic operations are performed in a manner corresponding to movements on an m-hour clock. The number  is called the modulus of the system. Let’s say we wanted to count to 53…

## Understanding Non-Base 10 Systems

In base-10, place values correspond to powers of 10, for example: In base-b, place values correspond to powers of b: Base-5 Base-5 uses the digits 0, 1, 2, 3, 4 to represent any number. In base-5, we start by counting 1, 2, 3, 4. At 5, however, we must write…

## The Mayan Numeration System

The Maya Indians had a numeration system based on the number 20. It used patterns of dots and bars to count, as shown: Q.   Convert 8,292 to Mayan notation. Answer:

## The Babylonian Numeration System

The Babylonian numeration system is based on powers of 60 (sexagesimal system). There are two symbols: Small numbers are represented much like the Egyptian system. For example: To represent larger numbers, use several groups of symbols, separated by spaces, and multiply the value of these groups by increasing powers of…

## The Chinese Numeration System

The Chinese system uses multiples of powers of 10 such as 10, 100, and 1,000. The system is a multiplicative system: numerals are formed by writing products of integers between 1 and 9 and powers of 10. Q1.   Express 二千 in Hindu-Arabic notation. Q2.   Express 九百四十二 in Hindu-Arabic notation. Q3.  …

## The Roman Numeration System

The Romans used letters of the alphabet as numerals. Q1.   Convert DCLXXVIII to Hindu-Arabic notation. Furthermore, if the value of a numeral is ever less than the value of the numeral to its right, then the value of the left numeral is subtracted from the value of the numeral to…

## The Egyptian Numeration System

In the Egyptian numeration system, numerals are formed by combining the symbols that represent various powers of ten: The value of the number is the sum of the values of the numerals. For example, the number 325 is represented as: The order of the symbols is not important, we could…