3.3.2 Converting between number bases

• What are number bases used for?

  Representing numbers
• The most common number bases include decimal, binary, and hexadecimal
• Decimal uses digits from 0 to 9.


  True
• Match the number base with its digits used:

  Decimal ↔️ 0-9

  Binary ↔️ 0-1

  Hexadecimal ↔️ 0-9, A-F
• Why is understanding number base conversions important in computer science?

  Computers use binary
• Binary uses only the digits 0 and 1.
• Steps to convert a decimal number to binary:

  1️⃣ Divide the decimal number by 2 and record the remainder

  2️⃣ Divide the result from step 1 by 2 and record the remainder

  3️⃣ Repeat step 2 until the result is 0

  4️⃣ The binary representation is the sequence of remainders, starting from the last one
• The binary representation of 25 is 11001.

  True
• To convert binary to decimal, multiply each digit by its corresponding power of 2 based on its position.
• The decimal value of binary 1011 is 11.


  True
• Which number base uses digits 0-9 and A-F?

  Hexadecimal
• To convert a decimal number to binary, you first divide by 2
• When converting from decimal to binary, the remainder is recorded at each division step.


  True
• Steps to convert a decimal number to binary

  1️⃣ Divide the decimal number by 2 and record the remainder

  2️⃣ Divide the result from step 1 by 2 and record the remainder

  3️⃣ Repeat step 2 until the result is 0

  4️⃣ The binary representation is the sequence of remainders, starting from the last one
• To convert a binary number to decimal, you multiply each digit by its corresponding power of 2
• When converting binary 1011 to decimal, the leftmost digit is multiplied by 2^3.

  True
• What is the decimal equivalent of binary 1011?

  11
• To convert a decimal number to hexadecimal, you divide by 16
• When converting to hexadecimal, remainders can be digits 0-9 or letters A-F.


  True
• Steps to convert a decimal number to hexadecimal

  1️⃣ Divide the decimal number by 16 and record the remainder

  2️⃣ Divide the result from step 1 by 16 and record the remainder

  3️⃣ Repeat step 2 until the result is 0

  4️⃣ The hexadecimal representation is the sequence of remainders, starting from the last one
• What is the hexadecimal representation of 7A3 in decimal?

  1955
• To convert from hexadecimal to decimal, multiply each digit by its corresponding power of 16
• In hexadecimal, the digit A represents 10 in decimal.


  True
• What is the first step in converting a hexadecimal number to decimal?

  Identify the hexadecimal digits
• What is the decimal equivalent of the hexadecimal number 7A3?

  1955
• Hexadecimal is used to represent binary data in a more compact and readable format.


  True
• Understanding number bases is crucial for data representation in computer systems.

  True
• Steps to convert a decimal number to binary

  1️⃣ Divide the decimal number by 2 and record the remainder

  2️⃣ Divide the result by 2 and record the remainder

  3️⃣ Repeat step 2 until the result is 0

  4️⃣ The binary representation is the sequence of remainders, starting from the last one
• When converting from decimal to binary, you divide by 2
• What is the binary representation of the decimal number 25?

  11001
• To convert from binary to decimal, you multiply each digit by its corresponding power of 2
• What is the decimal value of the binary number 1011?

  11
• When converting from decimal to hexadecimal, you divide by 16
• Hexadecimal uses 16 unique digits, including letters A-F.

  True
• Steps to convert a hexadecimal number to decimal

  1️⃣ Identify the hexadecimal digits

  2️⃣ Multiply each digit by the corresponding power of 16

  3️⃣ Sum the products to get the decimal equivalent
• What is the divisor used in the conversion process from decimal to hexadecimal?

  16
• To convert a hexadecimal number to decimal, multiply each digit by its corresponding power of 16
• Hexadecimal is used to represent binary data in a more compact format.


  True
• Steps to convert a binary number to hexadecimal

  1️⃣ Group the binary number into sets of 4 digits from right to left

  2️⃣ Add leading zeros if the last group has fewer than 4 digits

  3️⃣ Convert each group into its corresponding hexadecimal digit
• What is the binary equivalent of the hexadecimal number 3B?

  00111011