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
• What is an example of a rational number?

  4.5
• What is the key difference between rational and irrational numbers?

  Irrational numbers cannot be expressed as fractions
• What is an example of an irrational number?

  π
• 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 do ordinal numbers typically start 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
• Can zero be considered a rational number?

  Yes, zero is a rational number
• What type of numbers can be both positive and negative?

  Integers
• What is the relationship between rational numbers and integers?

  Integers are included in rational numbers
• How do natural numbers differ from real numbers in usage?

  Natural numbers are for counting, real numbers for measuring
• What are the two types of prefixes used to describe quantities of bytes?

  Binary prefixes and decimal prefixes
• How do binary prefixes increase in value?

  They go up in powers of two
• How do decimal prefixes increase in value?

  They go up in powers of ten
• What is an example of a decimal prefix?

  1 kilogram
• Why are binary prefixes not used as frequently as decimal prefixes?

  They have similar orders of magnitude
• What are the binary prefixes and their values?

  • Kibi (Ki): $2^{10} =$$1024$
  • Mebi (Mi): $2^{20} =$$1048576$
  • Gibi (Gi): $2^{30} =$$1073741824$
  • Tebi (Ti): $2^{40} \approx 1.0995 \times 10^{12}$
• What are the decimal prefixes and their values?

  • Kilo (K): $10^{3} =$$1000$
  • Mega (M): $10^{6} =$$1000000$
  • Giga (G): $10^{9} =$$1000000000$
  • Tera (T): $10^{12} =$$1 \times 10^{12}$
• How many bits are in 1 Kib?

  $1024 \text{ bits}$
• How many bytes are in 1 KiB?

  $1024 \text{ bytes}$
• How many bits are in 1 KiB?

  $8192 \text{ bits}$
• How many bytes are in 1 GB?

  $10^{9} \text{ bytes}$
• How many bits are in 1 GB?

  $8 \times 10^{9} \text{ bits}$
• What is the relationship between bytes and bits for binary prefixes?

  • 1 Kib = $2^{10} \text{ bits}$
  • 1 KiB = $2^{10} \text{ bytes} =$$8192 \text{ bits}$
  • 1 GB = $10^{9} \text{ bytes} =$$8 \times 10^{9} \text{ bits}$
• What is a character code?

  A decimal digit representing a character
• How does a primitive information coding system assign numbers to letters?

  It assigns numbers 1 to 26 to A to Z
• What binary representation corresponds to the decimal digit 13?

  1101
• What does ASCII stand for?

  American Standard Code for Information Interchange
• How many bits does ASCII use to represent characters?

  7 bits