Number Systems Overview

Definition of Number Systems

• A number system is a consistent way of representing numbers using digits or symbols.
• The value of each digit in a number is determined by its position and the base of the number system.
• Number systems are used for converting between different representations of numbers.
• Number systems help represent numbers using a limited set of symbols.

Types of Number Systems

• There are four main types of number systems:
  • Binary (Base 2)
  • Octal (Base 8)
  • Decimal (Base 10)
  • Hexadecimal (Base 16)

Octal Number System

• Uses eight digits: 0, 1, 2, 3, 4, 5, 6, 7.
• Has a base of 8.
• Has fewer digits compared to other systems, resulting in fewer computational errors.
• Examples: 358, 9238, 14183588

Decimal Number System

• Uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• Has a base of 10.
• Is the system used in everyday life.
• Numbers without a specified base are assumed to be decimal (base 10).
• Examples: 72310, 524710, 3210, 983710

Converting Binary to Decimal

• Step 1: Identify the base of the binary number.
• Step 2: Multiply each digit in the binary number by the corresponding power of 2, starting from the rightmost digit with an exponent of 0 and increasing by 1 for each position to the left.
• Step 3: Add the results from Step 2 to obtain the decimal equivalent.

Conversion Examples

• Example 1: Converting (100111)2 to decimal:
  • (1 × 2^5) + (0 × 2^4) + (0 × 2^3) + (1 × 2^2) + (1 × 2^1) + (1 × 2^0) = 32 + 0 + 0 + 4 + 2 + 1 = 39
• Example 2: Converting (111111)2 to decimal:
  • (1 × 2^5) + (1 × 2^4) + (1 × 2^3) + (1 × 2^2) + (1 × 2^1) + (1 × 2^0) = 32 + 16 + 8 + 4 + 2 + 1 = 63

Explore the various types of number systems, including binary, octal, decimal, and hexadecimal. Understand how these systems represent numbers and their application in computing. Test your knowledge on their characteristics and conversions!