Bits, Bytes and Binary Part Two: 1 + 1 = 10

Introduction

• Review of binary numbers and their significance in computing.
• Emphasis that this video involves some math, which is not typical for this course.
• Importance of understanding binary numbers in various contexts in computing.

Counting in Decimal

• Start with 0, add 1 to get 1.
• Continue adding 1 to each new number.
• Key point: Decimal system has 10 digits (0-9).
• Example: 8 + 1 = 9, 9 + 1 = 10 (carry the 1).
• Illustration continues up to 100, showing the concept of carrying over digits.

Counting in Binary

• Start with 0 + 1 = 1 (same as decimal).
• Key point: Binary system has 2 digits (0 and 1).
• Example: 1 + 1 = 10 (carry the 1).
• Continue adding 1, showing carrying over just like in decimal but within the binary system.
• List of first 8 binary numbers (0 to 7 in decimal).
• List of first 16 binary numbers (0 to 15 in decimal) and their decimal equivalents.

Distinguishing Number Systems

• Subscripts to indicate base (e.g., 6_10 and 110_2).
• Importance in disambiguating number systems.
• Notation helps especially with other number systems like octal (base 8) and hexadecimal (base 16).

Conversion Between Binary and Decimal

• Example with decimal: 1891 (explained with powers of 10).
• Example with binary: 1101 (explained with powers of 2).
• Highlight: Conversion understanding is helpful but not required for exams/quizzes.

Storing Information in Bits

• One bit: 2 combinations (0 or 1) - often represents true/false.
• Two bits: 4 combinations (00, 01, 10, 11).
• Three bits: 8 combinations.
• Four bits: 16 combinations.
• Use cases: Provinces of Canada in 4 bits vs. U.S. States needing more than 4 bits.

Formula for Combinations

• Formula: 2^n for n bits.
• Table showing combinations for 1 to 10 bits.
• Highlight: Bits can represent numbers, positive/negative values, or other data (e.g., dorms at Stanford).

Powers of Two in Real Life

• Common memory sizes (64MB, 128MB, 256MB) follow powers of two.
• Shopping for technology (like iPhones): memory sizes are powers of two.
• Explanation: Internally, computers use the binary system (base 2).

Kilobytes, Megabytes, and Beyond

• Distinction between powers of 10 (thousands, millions) and powers of 2.
• Kilobytes, megabytes, gigabytes, terabytes: base 2 equivalents.
• Higher orders: Peta, Exa, Zeta, Yotta.
• Note on communication speeds often using base 10 (electrical engineering).

Conclusion

• Next lecture: What goes wrong with binary numbers.