What is Boolean Algebra?

Boolean Algebra — Thuật ngữ

A branch of algebra operating on true/false values using AND, OR, NOT operators, foundational to digital logic.

Chi tiết kỹ thuật

Boolean Algebra answers 'to what power must the base be raised to produce this value?' Common bases: natural log (ln, base e ≈ 2.718), common log (log10), and binary log (log2, used in computing for bit-depth and information theory). Logarithmic scales are used for pH (chemistry), decibels (audio), Richter magnitude (seismology), and algorithm complexity analysis (O(log n)). The slide rule — the engineer's calculator before electronics — operated entirely on logarithmic principles.

Ví dụ

```
Logarithm identities:

  log_b(x) = y  means  b^y = x

  log₁₀(1000) = 3   (10³ = 1000)
  log₂(256)   = 8   (2⁸ = 256)
  ln(e)       = 1   (e¹ = e ≈ 2.718)

  log(a × b) = log(a) + log(b)
  log(a / b) = log(a) - log(b)
  log(a^n)   = n × log(a)
```

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Mean Median Standard Deviation Percentile Logarithm Factorial Fibonacci Sequence Prime Number GCD LCM Matrix Determinant Permutation Combination Derivative Integral Pythagorean Theorem Radians Modular Arithmetic Correlation Eigenvalue Exponential Fourier Transform Variance Mode Regression Probability Distribution Normal Distribution Sigmoid Function Interpolation (Math) Cross Product Dot Product Big O Notation Euler's Number Pi Complex Number Set Theory Bayes' Theorem Taylor Series Gradient Monte Carlo Method Least Squares Entropy (Information) Hamming Distance Newton's Method Z-Score Binomial Distribution