Base Converter

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Description

This MicroSim provides an interactive tool for converting numbers between arbitrary number bases from 2 to 36. It always displays the four primary bases used in digital design — binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — plus a user-selectable custom output base. It displays conversions in real-time and shows step-by-step conversion procedures to help students understand the underlying mathematics.

Key Features

  • ● Arbitrary base support for any base from 2 to 36 (input and output)
  • ● Real-time conversion to all bases as you type
  • ● Step-by-step display showing the conversion process
  • ● Two's complement support for signed 8-bit numbers
  • ● Input validation with helpful error messages

How to Use

  1. Enter a number in the input field
  2. Select the input base from the dropdown (any base from 2 to 36)
  3. Select an output base to see a custom conversion alongside the four standard bases
  4. View conversions instantly displayed for binary, octal, decimal, hex, and your custom base
  5. Enable Two's Complement checkbox to work with signed 8-bit numbers

Learning Objectives

Bloom Level: Apply (L3)  |  Bloom Verb: Calculate, convert, use

After using this MicroSim, students will be able to:

  • ✓ Convert numbers between any bases from 2 to 36
  • ✓ Understand positional notation and place values in different bases
  • ✓ Apply two's complement representation for signed numbers
  • ✓ Recognize the relationship between binary groupings and hex/octal digits

Lesson Plan

Before the Simulation (5 minutes)

  • ● Review positional notation concepts
  • ● Discuss why computers use binary and why hex is convenient for humans

During the Simulation (10 minutes)

  1. Convert a decimal number (e.g., 42) to all other bases
  2. Enter a binary number and observe the conversions
  3. Enable two's complement mode and enter negative decimal numbers
  4. Observe how 8-bit binary representations handle negative values

After the Simulation (5 minutes)

  • ● Practice mental conversion of small numbers
  • ● Discuss when each base is most useful in practice

References