Fundamentals of Data Representation

• What is the set of natural numbers denoted by?

  ℕ
• What does the set ℕ of natural numbers include?

  All positive whole numbers and zero
• What is the set of integers denoted by?

  ℤ
• What does the set ℤ of integers include?

  Whole numbers, both positive and negative
• What is the set of rational numbers denoted by?

  ℚ
• What defines a rational number?

  Can be expressed as a fraction
• Can zero be considered a rational number?

  Yes
• What is the definition of an irrational number?

  Cannot be expressed as a fraction
• What is the set of real numbers denoted by?

  ℝ
• What does the set ℝ of real numbers include?

  All natural, rational, and irrational numbers

  
• What are ordinal numbers used for?

  To describe numerical positions of objects
• How are ordinal numbers typically indexed in arrays?

  Starting with an element in position 0
• What is the difference between counting and measuring in terms of number sets?

  • Counting: Use natural numbers (ℕ)
  • Measuring: Use real numbers (ℝ)
• What is the symbol for natural numbers?

  ℕ
• What is the symbol for integers?

  ℤ
• What is the symbol for rational numbers?

  ℚ
• What is the symbol for real numbers?

  ℝ
• What type of numbers can be used for counting?

  Natural numbers
• What type of numbers should be used for measurement?

  Real numbers
• What is the fundamental unit of information?

  Bit
• How many bits are in a byte?

  8 bits
• How many different values can be represented with n bits?

  2$^n$
• What is a nybble?

  Half a byte (4 bits)
• How is a bit notated?

  Lowercase b
• How is a byte notated?

  Uppercase B
• How many bits are in 3 bytes?

  24 bits
• What happens to the number of values represented as bits increase?

  The number of values increases
• How many different values can be represented with 2 bits?

  4 values
• What is the range of values dependent on?

  Number of bits
• What are the two types of prefixes used to describe quantities of bytes?

  Binary and decimal prefixes
• How do binary prefixes differ from decimal prefixes?

  Binary prefixes use powers of 2
• What is the binary prefix for 1024 bytes?

  Kibi (Ki)
• What is the decimal prefix for 1000 bytes?

  Kilo (k)
• What is the binary prefix for 1,048,576 bytes?

  Mebi (Mi)
• What is the decimal prefix for 1,000,000 bytes?

  Mega (M)
• What is the binary prefix for 1,073,741,824 bytes?

  Gibi (Gi)
• What is the decimal prefix for 1,000,000,000 bytes?

  Giga (G)
• What is the binary prefix for approximately 1.0995×10$^{12}$ bytes?


  Tebi (Ti)
• What is the decimal prefix for 1,000,000,000,000 bytes?

  Tera (T)
• How many bits are in 1 kibibyte?

  8192 bits