Number Systems

Numeral System

• A numeral system represents a useful set of numbers, reflecting a number's arithmetic and algebraic structure, and offers a standard representation.

History of Numeral System

• The concept of numbers originated from counting quantities in the environment, dating back to the early days of civilization.
• People may have initially used strokes on the bark of a tree to count, later switching to using their fingers, which formed the basis of a decimal number system.

Decimal Number System

• The decimal number system is based on ten and has ten numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
• Any higher number can be formed with a combination of these numerals.
• Each of the ten numerals is called a digit.

Number System Characteristics

• The base or radix of a number system indicates the number of distinct symbols or numerals used to represent quantities.
• The decimal number system has a base of ten, while the binary number system has a base of two.

Binary Number System

• The binary number system is a base-2 system, using only two numerals: 0 and 1.
• The binary system is more convenient for digital electronic systems than the decimal system.
• The two numerals in the binary system can be represented with simple devices, such as a light switch with two sides.