Binary-and-Denary-Numbers presentation
- 1. Binary and Denary Numbers: The Language of Computers
- 2. Learning Objectives • Understand the differences between base 2 and base 10 • Learn how to read and write numbers in binary and denary • Convert numbers between binary and denary • Use place value tables for both number systems
- 3. What is Denary (Base 10)? • The number system we use every day • Uses digits 0-9 • Called "base 10" because it has 10 different digits • Example: 123 is one hundred and twenty-three • We use this because humans have 10 fingers!
- 4. What is Binary (Base 2)? • The language of computers • Uses only two digits: 0 and 1 • Called "base 2" because it has 2 different digits • Think of it like switches: ON (1) or OFF (0) • Used by computer processors (CPU)
- 5. Place Values in Denary Powers of 10: • Ones: 10^0 = 1 • Tens: 10^1 = 10 • Hundreds: 10^2 = 100 • Thousands: 10^3 = 1000
- 6. Denary Example Number: 1977 • 1 thousand (1 × 10^3) • 9 hundreds (9 × 10^2) • 7 tens (7 × 10^1) • 7 ones (7 × 10^0)
- 7. Place Values in Binary Powers of 2: • 2^0 = 1 • 2^1 = 2 • 2^2 = 4 • 2^3 = 8 • 2^4 = 16
- 8. Binary Place Value Table 8-bit binary number: • 2^7 = 128 • 2^6 = 64 • 2^5 = 32 • 2^4 = 16 • 2^3 = 8 • 2^2 = 4 • 2^1 = 2 • 2^0 = 1
- 9. Converting Binary to Denary Example: 10100000 • 1 × 2^7 = 128 • 0 × 2^6 = 0 • 1 × 2^5 = 32 All others = 0 Total: 128 + 32 = 160
- 10. Converting Denary to Binary Example: Convert 46 to binary • 32 (2^5) + 8 (2^3) + 4 (2^2) + 2 (2^1) Result: 00101110
- 11. Important Rules • 8-bit binary can only show numbers up to 255 • Each position can only be 0 or 1 • Think of each digit as a switch • Add the values where you see 1
- 12. Real World Connection • Computer memory uses binary • Digital storage (files, photos) • Computer processors • All computer calculations happen in binary
- 13. Practice Example 1 Convert binary 11000101 to denary: • 128 + 64 + 4 + 1 = 197
- 14. Practice Example 2 Convert denary 25 to binary: • 16 + 8 + 1 = 00011001
- 15. Review Questions • Convert binary 10101010 to denary • Convert denary 50 to binary • What's the largest number you can make with 8 bits? Remember to review all answers carefully as some calculations may need verification.