# Gray Code and Thermometer BCD Encoder Visualizer

Convert an N-bit value to binary, Gray, one-hot and thermometer codes with a counting truth table, Hamming-distance chart and Verilog/VHDL encoder stubs.

> Canonical page: https://elysiatools.com/en/tools/gray-code-and-thermometer-bcd-encoder-visualizer

- **Category:** Development

- **Keywords:** gray code converter, thermometer code, one-hot encoding, hamming distance chart, binary to gray verilog, flash adc thermometer, async fifo gray pointer, unit distance code

## Overview

A digital-design visualizer for binary-code alternatives on words of 2–6 bits.

Encodings produced simultaneously for the chosen value: plain binary; Gray/reflected code (G = B XOR (B >> 1), the unit-distance code whose adjacent values — including the wrap — differ in exactly one bit); one-hot (2ⁿ bits, a single 1); and thermometer/unary (2ⁿ−1 bits, MSB-aligned, the native flash-ADC comparator output).

The Hamming-distance chart walks every counting transition and shows the hazard directly: binary flips up to all n bits at carry boundaries (0111→1000), Gray and thermometer never flip more than one bit, one-hot always flips exactly two. A full counting truth table doubles as the Karnaugh-map axis order and rotary-encoder disc pattern.

Ready-to-paste HDL stubs: parameterized Verilog and VHDL modules with binary→Gray (XOR), binary→one-hot (sized shift), binary→thermometer (MSB-aligned unary shift), and the Gray→binary cascading-XOR decoder.

## Inputs

- **Word Width (bits)** (select)
- **Input Value (decimal)** (number): 11
- **HDL Stub Language** (select)
- **Show Full Counting Sequence Table** (checkbox)

## When to use

- Designing asynchronous FIFO pointers or clock domain crossing logic that require unit-distance Gray codes to eliminate multi-bit sampling glitches.
- Modeling flash ADC comparator outputs and verifying thermometer-to-binary or thermometer-to-Gray encoder logic.
- Evaluating state machine encoding schemes to compare bit-switching activity and Hamming distances between binary, one-hot, and Gray implementations.

## How it works

- Select the word width between 2 and 6 bits and enter the decimal value to convert.
- Choose the desired HDL stub language (Verilog, VHDL, or both) and toggle the full counting sequence table option.
- Inspect the resulting binary, Gray, one-hot, and thermometer codes alongside transition bit flips, the Hamming-distance chart, and synthesizable HDL modules.

## Use cases

- Asynchronous FIFO pointer synchronizer design and verification.
- Flash ADC thermometer code conversion and decoder logic drafting.
- Rotary encoder disc layout mapping and unit-distance transition analysis.

## Frequently asked questions

### What word widths does the visualizer support?

The visualizer supports word widths from 2 bits (values 0–3) up to 6 bits (values 0–63).

### Why do Gray and thermometer codes prevent multi-bit switching hazards?

Adjacent values in Gray and thermometer codes differ by only one bit per step (Hamming distance of 1), preventing intermediate sampling errors at counter boundaries.

### How is binary converted to Gray code?

Binary values are converted to Gray code using the standard bitwise equation G = B XOR (B >> 1).

### What is the difference between one-hot and thermometer encoding?

One-hot sets exactly one active high bit across 2ⁿ bit positions, while thermometer code fills an MSB-aligned continuous run of 1s across 2ⁿ−1 bits.

### What HDL code templates are provided?

The tool outputs parameterized Verilog and VHDL modules for binary-to-Gray, binary-to-one-hot, binary-to-thermometer encoders, and cascading XOR Gray-to-binary decoders.

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