Number systems are mathematical systems used to represent and manipulate numbers. They provide a way to express quantities and perform arithmetic operations. While there are various number systems, the most commonly used ones are the decimal, binary, octal, and hexadecimal systems.

Decimal System (Base-10)

• The decimal system is the most familiar number system, used in everyday life.
• It has a base of 10, meaning it uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
• Each digit's position represents a power of 10.

In the number 256, the digit 2 represents 2 x 10² (hundreds place), the digit 5 represents 5 x 10¹ (tens place), and the digit 3 represents 6 x 10⁰ (ones place).

Binary System (Base-2)

• The binary system is fundamental in computing and digital electronics.
• It has a base of 2, using only two digits: 0 and 1.
• Each digit's position represents a power of 2.

In the binary number 101, the digit 1 represents 1 x 2² (fourth place), the digit 0 represents 0 x 2¹ (second place), and the digit 1 represents 1 x 2⁰ (first place).

Octal System (Base-8)

• The octal system is less commonly used but still finds applications in some areas.
• It has a base of 8, using eight digits: 0, 1, 2, 3, 4, 5, 6, and 7.
• Each digit's position represents a power of 8.

in the octal number 346, the digit 3 represents 3 x 8² (64s place), the digit 4 represents 4 x 8¹ (eights place), and the digit 6 represents 6 x 8⁰ (ones place).

Hexadecimal System (Base-16)

• The hexadecimal system is widely used in computer programming and digital systems.
• t has a base of 16, using sixteen digits: 0-9 and A-F, where A represents 10, B represents 11, and so on up to F representing 15.

• Each digit's position represents a power of 16.

In number 3A7, the digit 3 represents 3 x 16² (256s place), the digit A represents 10 x 16¹ (sixteens place), and the digit 7 represents 7 x 16⁰ (ones place).

Summary