Binary Division Simulator — Restoring & Non-Restoring Division

An interactive Computer Organization and Architecture (COA) educational web application that teaches and simulates unsigned binary division step-by-step.

By Roshwin Niketh M

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Purpose

Unlike a simple binary calculator, this simulator acts as a patient teaching guide. It breaks every iteration down into hardware register micro-steps—explaining the combined [A, Q] left shift, vertical binary subtraction/addition, two's-complement sign checking on accumulator A, quotient-bit (Q₀) decisions, restoration vs. non-restoring compensation, and final remainder verification.

Algorithms Supported

1. Restoring Division Algorithm (Unsigned)
2. Non-Restoring Division Algorithm (Unsigned)

Scope Note: This simulator demonstrates unsigned binary division (4-bit, 8-bit, and 16-bit operands). Signed division requires additional sign-handling rules and is outside the current simulation.

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Key Features

• Teacher-Style Micro-Steps: Every cycle is decomposed into 5 pedagogical micro-steps (plus a dedicated post-loop Final Correction step in Non-Restoring Division).
• Live Hardware Registers: Displays A ($n+1$ bits), Q ($n$ bits), M ($n$ bits and $(n+1)$-bit zero-extended), Q₀, and Count with explicit NEGATIVE / NON-NEGATIVE sign badges.
• Combined Shift Visualizer: Illustrates how Q's most-significant bit crosses into A's least-significant bit during Left Shift [A, Q].
• Vertical Binary Arithmetic: Shows both register-level subtraction/addition (A - M, A + M) and two's-complement hardware adder views (A + (-M)).
• Interactive Controls: Previous Step, Next Step, Auto Play, Pause, Restart, Show All Steps, and a step scrubber.
• Complete Cycle Trace Table: Summarizes every cycle and allows clicking any row to jump directly to that cycle.
• Mathematical Verification: Confirms Dividend = Divisor × Quotient + Remainder and 0 ≤ Remainder < Divisor.

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Why Accumulator A Uses $n + 1$ Bits

For an $n$-bit unsigned dividend Q and $n$-bit unsigned divisor M:

• Register A (the partial remainder) is $(n + 1)$ bits wide, and M is zero-extended to $(n + 1)$ bits during arithmetic with A.
• After shifting [A, Q] left by 1 bit and subtracting or adding M, the signed partial remainder always satisfies $-M \le A < M$, which lies strictly within $[-(2^n - 1), 2^n - 2] \subset [-2^n, 2^n - 1]$.
• Using $n + 1$ bits in two's-complement representation guarantees that A's most-significant bit (MSB) is always the true sign bit without signed overflow.

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Technology Stack

• React 18
• TypeScript
• Vite
• Plain CSS (Responsive white-and-blue academic theme)
• Vitest (Automated unit & exhaustive verification tests)

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Architecture & Modular Reusability

The codebase separates pure algorithm simulation engines from the React presentation layer so the division modules can be directly imported into a larger Computer Organization and Architecture simulator:

src/
├── lib/
│   ├── binary.ts                 # BigInt fixed-width binary & two's-complement utilities
│   ├── restoringDivision.ts      # Pure Restoring Division engine & trace generator
│   └── nonRestoringDivision.ts   # Pure Non-Restoring Division engine & trace generator
├── types/
│   └── division.ts               # Structured trace, micro-step, and register interfaces
├── components/                   # Reusable COA register, shift, arithmetic, and trace UI
├── simulators/                   # Restoring & Non-Restoring simulator views
└── tests/                        # Unit + exhaustive 4-bit (240 pairs × 2) + 8/16-bit tests

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Getting Started

Installation

npm install

Run Locally (Development Server)

npm run dev

Run Automated Tests

npm test

Production Build

npm run build