Number System in Computers

Number System in Computers

A number system is a way to represent numbers using digits or symbols in a consistent manner. In computers, data is represented using different number systems, most importantly the binary system. Below are the commonly used number systems in computing:

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1. Binary Number System (Base-2)

• Digits used: 0, 1
• Base: 2
• Use: All data in computers (text, images, audio) is ultimately stored and processed in binary.
• Example:
  Decimal 5 = Binary 101

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2. Decimal Number System (Base-10)

• Digits used: 0 to 9
• Base: 10
• Use: This is the number system used by humans in everyday life.
• Example:
  Decimal 123 means:
  (1×10²) + (2×10¹) + (3×10⁰) = 100 + 20 + 3

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3. Octal Number System (Base-8)

• Digits used: 0 to 7
• Base: 8
• Use: Sometimes used in older computer systems and shorthand for binary.
• Example:
  Binary 101110 = Octal 56

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4. Hexadecimal Number System (Base-16)

• Digits used: 0 to 9 and A to F (where A=10, B=11,...F=15)
• Base: 16
• Use: Compact representation of binary numbers, widely used in programming and digital electronics.
• Example:
  Binary 11111111 = Hexadecimal FF

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Conversion Example:

Let’s convert Decimal 25 to Binary:

• Divide by 2 repeatedly and record the remainders:

  25 ÷ 2 = 12 remainder 1  
  12 ÷ 2 = 6  remainder 0  
  6  ÷ 2 = 3  remainder 0  
  3  ÷ 2 = 1  remainder 1  
  1  ÷ 2 = 0  remainder 1  
  

• Binary = 11001

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Summary Table:

Number System	Base	Digits Used	Example (Decimal 15)
Binary	2	0, 1	1111
Decimal	10	0–9	15
Octal	8	0–7	17
Hexadecimal	16	0–9, A–F	F

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