Class Notes: Range of Integers

Introduction

• Welcome to Nesso Academy.
• Previous lecture covered the importance of data types in C++.
• Current lecture focuses on understanding and deriving the formula for the range of integers.
• Importance: In future lectures, we will discuss fundamental data types and their ranges.

Objective

• Learn to calculate the range of integers.

Topics Covered

• Deriving the Formula for Integer Range:

  • Consider a simplified integer data type of size three bits.
  • Calculate range through binary numbers and their combinations:
    • Possible binary combinations: 000, 001, 010, 011, 100, 101, 110, 111
    • Interpretation as positive integers: 0 to 7.
  • Explanation for derivation:
    • Positional weighting of bits: 4, 2, and 1.
    • Example calculation: 111 becomes 4 + 2 + 1 = 7.

• Range for Both Positive and Negative Integers:

  • Sign bit representation:
    • 0 indicates positive, 1 indicates negative.
  • Formula for range:
    • Using three bits, range is -4 to +3.
  • Derivation for range:
    • Formula: -2^(n-1) to 2^(n-1) - 1.
    • Example conversion for three bits yield above range.

Formula Summary

• Positive Values Range:
  • General formula for n bits: 0 to 2^n -1.
• Both Positive and Negative Values Range:
  • General formula for n bits: -2^(n-1) to 2^(n-1) - 1.

Conclusion

• Successfully derived formulas to calculate the range of integers.
• Next lecture will cover fundamental data types in C++.

Next Steps

• Prepare for understanding fundamental data types and their applications in C++ in the upcoming session.

[Applause] [Music]