Decimal Number System

What is Decimal Number System?

Decimal number system is the most common example of positional notational number system and all the arithmetical calculations undertaken by human being are carried out on the basis of this number system. In this system, the symbols used are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and the base is 10. Thus the number

d_n-1 d_n-2…..d ₁ d₀ means d_n-1 10^n-1 + d_n-2 10^n-2 + ……. + d₁ 10¹ + d₀ 10⁰

and this is an n-digit number. If the number be extended to the right of the decimal point, then the powers of the base will be negative starting from -1.

For example, the number 3528 has the magnitude

3528 = 3 × 10³ + 5 × 10² + 2 × 10¹ + 8 × 10⁰

and the number 26.57 has the magnitude

26.57 = 2 × 10 + 6 × 10⁰ + 5 × 10^-1 + 7 × 10^-2

● Binary Numbers

• Data and Information

• Number System

• Decimal Number System

• Binary Number System

• Why Binary Numbers are Used

• Binary to Decimal Conversion

• Conversion of Numbers

• Octal Number System

• Hexa-decimal Number System

• Conversion of Binary Numbers to Octal or Hexa-decimal Numbers

• Octal and Hexa-Decimal Numbers

• Signed-magnitude Representation

• Radix Complement

• Diminished Radix Complement

• Arithmetic Operations of Binary Numbers

• Binary Addition

• Binary Subtraction

• Subtraction by 2’s Complement

• Subtraction by 1’s Complement

• Addition and Subtraction of Binary Numbers

• Binary Addition using 1’s Complement

• Binary Addition using 2’s Complement

• Binary Multiplication

• Binary Division

• Addition and Subtraction of Octal Numbers

• Multiplication of Octal Numbers

• Hexadecimal Addition and Subtraction

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