5.3 Data representation

• What are the digits used in the binary number system?

  0 and 1
• The base of the binary number system is 2
• The binary number system is directly suitable for computers because it aligns with voltage levels.
• Match the advantage of using binary in computers with its description:

  Simple implementation ↔️ Uses only two states: on/off

  High reliability ↔️ Low number of states reduces errors

  Efficient data storage ↔️ Requires minimal memory space
• How many digits does the hexadecimal number system use?

  16
• The digits in the hexadecimal system include 0-9 and A-F
• Each hexadecimal digit corresponds to four binary digits.
• Steps to convert a binary number to decimal:

  1️⃣ Identify each digit's place value (powers of 2 from right to left)

  2️⃣ Multiply each digit by its place value

  3️⃣ Sum the products
• To convert a decimal number to binary, you divide by 2
• What is the value of the hexadecimal digit A in decimal?

  10
• When converting binary to hexadecimal, you group the binary digits into sets of four.
• Match the conversion type with its method:

  Binary to Decimal ↔️ Multiply by powers of 2

  Decimal to Binary ↔️ Divide by 2 repeatedly

  Hexadecimal to Decimal ↔️ Multiply by powers of 16

  Decimal to Hexadecimal ↔️ Divide by 16 repeatedly

  Binary to Hexadecimal ↔️ Group into sets of four

  Hexadecimal to Binary ↔️ Convert each digit to four bits
• Why is hexadecimal useful for representing binary data?

  Uses fewer digits
• Hexadecimal numbers are easy to convert to binary numbers.
• The hexadecimal number system is a base-16
• Match the number system with its base:

  Hexadecimal ↔️ 16

  Decimal ↔️ 10

  Binary ↔️ 2
• The digits in the hexadecimal number system are 0-9 and A-F
• The decimal number system is the natural language of digital circuits.

  False
• What is the method for converting a binary number to decimal?

  Multiply by powers of 2
• To convert a decimal number to binary, you divide by 2
• Steps to convert a decimal number to binary:

  1️⃣ Divide the decimal number by 2

  2️⃣ Record the remainder (0 or 1)

  3️⃣ Repeat the division until the quotient is 0

  4️⃣ Write the remainders in reverse order
• What is the method for converting a hexadecimal number to decimal?

  Multiply by powers of 16
• To convert a decimal number to hexadecimal, you divide by 16
• How do you convert a binary number to hexadecimal?

  Group in sets of four
• Converting a hexadecimal digit to binary involves writing four bits for each digit.
• Match the number system with its conversion method:

  Binary to Decimal ↔️ Multiply by powers of 2

  Decimal to Hexadecimal ↔️ Divide by 16 and record remainders

  Hexadecimal to Binary ↔️ Convert each digit to four bits

  Decimal to Binary ↔️ Divide by 2 and record remainders
• Unsigned integers can only represent non-negative values.
• Unsigned integers use one bit to indicate the sign of the number.

  False
• What are the two main components of floating-point representation?

  Mantissa and exponent
• Floating-point numbers are suitable for scientific and engineering calculations.
• Floating-point numbers have unlimited precision.

  False
• Floating-point numbers are often represented in normalized form to ensure maximum precision
• Floating-point numbers can represent fractions and decimals, unlike integers.
• Floating-point numbers have limited precision due to a fixed number of bits for the mantissa and exponent
• What is an example of a floating-point number in normalized form?

  $1.234 \times 10^{5}$
• Character encoding standards define how text characters are represented as binary values in computers.
• ASCII supports only 128 characters and has a range from 0 to 127.
• How many characters does Unicode support?

  Over 143,000
• Order the following encoding standards based on compatibility with ASCII:

  1️⃣ UTF-8

  2️⃣ ASCII
• What is an advantage of using Unicode in multilingual documents?

  Supports vast range of characters