5.1 Number systems

• What is a number system in mathematics?

  Method for representing numbers
• A number system uses a set of symbols called digits and a base known as radix
• The decimal number system has a base of 10.
• The binary number system uses digits 0 and1.
• Match the number system with its base:

  Hexadecimal ↔️ 16

  Octal ↔️ 8

  Decimal ↔️ 10

  Binary ↔️ 2
• What does each position in a binary number represent?

  Power of 2
• The binary number system uses only the digits 0 and 1
• A bit is a digit in the binary number system.
• What is the decimal equivalent of $1011_{2}$?


  $11_{10}$
• The binary number system is used in computer processing and storage.
• What is the base of the decimal number system?

  10
• The decimal number system uses digits 0 through 9
• Match the positional value with its number system:

  Powers of 10 ↔️ Decimal

  Powers of 2 ↔️ Binary
• The decimal number system is used in everyday arithmetic.
• What determines the number of unique digits in a number system?

  Base or radix
• Common number systems include decimal, binary, hexadecimal, and octal
• Match the number system with its digits:

  Binary ↔️ 0, 1

  Hexadecimal ↔️ 0-9, A-F

  Octal ↔️ 0-7

  Decimal ↔️ 0-9
• The binary number system is fundamental for computer storage and processing.
• In which older systems is the octal number system still used?

  Some older systems
• What base is the decimal number system?

  10
• The decimal number system uses digits from 0 to 9
• What does each digit's position in the decimal number system represent?

  Power of 10
• Where is the decimal number system used in everyday life?

  Arithmetic
• Each position in the decimal number system represents a power of 10
• The decimal number system is a base-10 system.
• Match the feature with the corresponding number system:

  Base 10 ↔️ Decimal

  Base 2 ↔️ Binary
• What are the digits used in the binary number system?

  0 and 1
• In the binary number system, the positional value is a power of 2
• What is the base of the binary number system?

  2
• The digits used in the binary number system are 0 and 1.
• What is the positional value of each digit in the binary number system?

  Powers of 2
• The decimal number 123 can be broken down as (1 \times 10^{2}) + (2 \times 10^{1}) + (3 \times 10^{0})</latex>.
• What is the base of the decimal number system?

  10
• In the decimal number system, each position represents a power of 10
• The decimal number system uses digits 0-9 and each position is a power of 10.
• Match the number system with its base:

  Decimal ↔️ 10

  Binary ↔️ 2

  Hexadecimal ↔️ 16

  Octal ↔️ 8
• What is the base of the hexadecimal number system?

  16
• The hexadecimal number system uses digits 0-9 and the letters A-F
• The hexadecimal number system simplifies binary data representation in computers.
• Arrange the following number systems in order of their bases from lowest to highest:

  1️⃣ Binary

  2️⃣ Octal

  3️⃣ Decimal

  4️⃣ Hexadecimal