Math & Logic Tools

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🧮 Math & Logic Tools

Expression evaluator, base converter, bitwise operations, percentages, Roman numerals, and ASCII reference.

🔢 Expression Calculator

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Usage Guide

What it does

Safely evaluates mathematical expressions without using eval(). Supports arithmetic, exponents, functions, and constants.

Supported Operators

  • + - * / % (modulo) ^ (power)
  • Parentheses for grouping: ( )

Supported Functions

  • sqrt(x), abs(x), floor(x), ceil(x), round(x)
  • sin(x), cos(x), tan(x) — radians
  • log(x) — natural logarithm

Constants

  • PI = 3.14159…
  • E = 2.71828…

Examples

2 + 3 * (4 - 1) / 2       → 6.5
sqrt(144) + 10             → 22
2 ^ 10                     → 1024
sin(PI / 2)                → 1
abs(-42) + floor(3.7)      → 45
log(E ^ 3)                 → 3

🔄 Binary / Decimal / Hex / Octal Converter

Input Base
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Usage Guide

What it does

Converts a number between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Supports negative numbers.

How to use

  • Select the input base from the dropdown
  • Enter a number → click Convert
  • All 4 base representations are shown, plus bit length

Examples

Input:   255 (Decimal)
Decimal: 255
Binary:  11111111
Octal:   377
Hex:     FF
Bits:    8

Negative Numbers

Prefix with - (e.g. -42). Results show signed representation.

Real-World Use Cases

  • Debugging bitwise operations in code
  • Reading hardware register values (hex → binary)
  • Network subnet mask conversion
  • Understanding file permissions (octal)

⚙️ Bitwise Calculator

Number A
Operation
Number B
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Usage Guide

What it does

Performs bitwise operations on two integers and shows the result in decimal, binary, and hex. Includes a bit-by-bit visualization.

Operations

  • AND (&) — both bits must be 1
  • OR (|) — either bit is 1
  • XOR (^) — exactly one bit is 1
  • NOT (~) — flips all bits (unary, uses only A)
  • << — shift bits left by B positions
  • >> — shift bits right by B positions

Example

A:   170  (10101010)
B:    85  (01010101)
AND:   0  (00000000)
OR:  255  (11111111)
XOR: 255  (11111111)

Real-World Use Cases

  • Masking bits in hardware registers
  • Setting/clearing/toggling flags
  • Calculating subnet masks (IP networking)
  • Optimized multiply/divide by powers of 2 (shift)

📊 Percentage Calculator

Mode
X (percentage)
Y (total)
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Usage Guide

What it does

Three percentage calculation modes to cover common use cases.

Modes

  • X% of Y — “What is 25% of 200?” → 50
  • X is what % of Y — “50 is what % of 200?” → 25%
  • % change from X to Y — “Change from 80 to 100?” → +25%

Examples

Mode: X% of Y
X = 15,  Y = 300  →  45

Mode: X is what % of Y
X = 75,  Y = 300  →  25%

Mode: % change from X to Y
X = 80,  Y = 100  →  +25%

Real-World Use Cases

  • Calculating discounts, tax, tips
  • Measuring performance improvement (% change)
  • Budget allocation and ratio analysis

🏛️ Roman Numeral Converter

Decimal (1–3999)
Roman Numeral
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Usage Guide

What it does

Converts between decimal numbers (1–3999) and Roman numerals. Validates Roman numeral syntax.

Roman Numeral Reference

I = 1      V = 5      X = 10
L = 50     C = 100    D = 500
M = 1000

Subtractive Rules

  • IV = 4, IX = 9
  • XL = 40, XC = 90
  • CD = 400, CM = 900

Examples

2024  →  MMXXIV
1999  →  MCMXCIX
XLII  →  42
DCCCLXXXVIII → 888

Real-World Use Cases

  • Copyright year formatting
  • Outline numbering (I, II, III…)
  • Super Bowl numbering, clock faces

📋 ASCII Table

Usage Guide

What it does

Searchable reference of all 128 ASCII characters showing decimal, hex, octal, binary, character, and description.

How to use

  • Scroll through the full table or use the search bar
  • Search by character (e.g. A), decimal code (e.g. 65), hex (e.g. 41), or description (e.g. space)

Key Ranges

0–31:    Control characters (NUL, TAB, LF, CR…)
32–47:   Symbols and punctuation
48–57:   Digits 0–9
65–90:   Uppercase A–Z
97–122:  Lowercase a–z
127:     DEL

Real-World Use Cases

  • Debugging character encoding issues
  • Writing parsers and lexers
  • Understanding control characters in protocols
  • Converting between character representations