3.3.1 Number bases

• Which digits are used in the decimal number system?

  0-9
• The binary number system uses digits 0 and 1.
• What is the place value of the digit 1 in the number 123?

  Hundreds
• Order the following number bases by the number of digits they use, from fewest to most.

  1️⃣ Binary

  2️⃣ Decimal

  3️⃣ Hexadecimal
• The hexadecimal number system is used to represent binary data in a more compact format.
• The binary number system uses only the digits 0 and 1.
• The decimal number system is used for everyday calculations.


  True
• What is the most commonly used base in the decimal number system?

  Base 10
• The binary number system is also known as base 2.
• How many digits does the binary number system use?

  Two
• The binary number system is essential in computer science because computers use it to store and process data.


  True
• In hexadecimal, the digit A represents the decimal value 10.
• What is the decimal equivalent of the hexadecimal number 2B?

  43
• The decimal number system uses powers of 10 for its place values.


  True
• In the decimal number 123, the digit 1 is in the hundreds place.
• What does 'base 10' denote in the decimal system?

  Powers of 10
• Arrange the place values in the decimal system from least to greatest:

  1️⃣ Ones

  2️⃣ Tens

  3️⃣ Hundreds

  4️⃣ Thousands
• In the binary number system, each digit represents a power of 2.
• To convert a decimal number to hexadecimal, you divide by 16 and keep track of the remainders.

  True
• The decimal number 200 converts to the hexadecimal number C8.
• What is the decimal equivalent of the hexadecimal number 3A?

  58
• What is the primary use of the hexadecimal number system?

  Compact binary data
• Number bases are different systems used to represent numbers.
• Match the number base with its digits:

  Binary ↔️ 0, 1

  Decimal ↔️ 0-9

  Hexadecimal ↔️ 0-9, A-F
• The binary number 1011 translates to 11 in decimal.

  True
• Match the hexadecimal digit with its decimal value:

  A ↔️ 10

  B ↔️ 11

  C ↔️ 12

  D ↔️ 13

  E ↔️ 14

  F ↔️ 15
• The hexadecimal number 2B converts to the decimal number 43.
• To convert a decimal number to binary, you divide by 2 and keep track of the remainders.


  True
• What is the binary equivalent of the decimal number 25?

  11001
• To convert a binary number to decimal, you multiply each digit by its corresponding power of 2.
• What is the decimal equivalent of the binary number 10110?

  22