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BCD to Decimal & Decimal to BCD Converter Studio

Welcome to the BCD encoding Studio, type binary coded decimals or standard integers to instantly visualize electronic signals.

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🔒 100% Client-Side
Binary Coded Decimal (BCD - 4 bits per digit)
Decimal Integer Value (Base-10)
Pure Binary Equivalent (Base-2)

Modifying any field automatically synchronizes the rest in real-time. Spaces are automatically handled.

Equivalence Outcomes

91

Step-by-Step Nibble Expansion

A walkthrough of character-to-binary mapping

1
Nibble 1 (1001)
Binary 1001 ➔ Digit: 9
2
Nibble 2 (0001)
Binary 0001 ➔ Digit: 1

Premium Study Presets & Benchmarks

Click any preset to instantly load and visualize its BCD register representation

BCD Digit Reference Table

Quick reference guide of the standard 4-bit numeral mappings

Decimal DigitBCD representation (8421)Pure Binary RepresentationASCII Character MappingWeight Classification
000000NUL (Null character)All bits inactive
100011SOH (Start of Header)LSB active
2001010STX (Start of Text)Power of 2
40100100EOT (End of Transmission)Power of 2
810001000BS (Backspace)Power of 2
910011001HT (Horizontal Tab)Max BCD digit limit

Understanding Binary Coded Decimal translation systems

Explore the architectural rules, hardware representations, and logical properties of BCD (8421) and standard Base-10 systems.

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The 4-Bit BCD Digit Rule

Unlike pure binary which represents the entire number as a single block of base-2 bits, Binary Coded Decimal maps each decimal digit separately into 4 bits (a nibble).

Rule:1 Decimal Digit = 1 BCD Nibble (4 bits).
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Hardware Clock Systems

Real-time clocks (RTC) and seven-segment displays heavily rely on BCD. Since it maps directly to individual digits, displaying BCD on screen requires no division instructions inside the CPU.

Application: Embedded hardware counters, timers, and legacy microcontrollers.
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100% Client-Side Privacy

Your security is fully guaranteed. All conversion and parsing takes place offline inside your browser window. Zero data packets are dispatched to external cloud APIs.

Privacy: Sandboxed client-side BigInt browser conversion engine.

Overview & Capabilities

Convert Binary Coded Decimal (8421 BCD) into Decimal numbers and decimals into BCD with our BCD to Decimal Converter! Supporting standard Packed and Unpacked BCD formats, our tool validates 4-bit nibble digit encodings ($0000_2$ to $1001_2$) and flags invalid pseudo-tetrades ($1010_2$ to $1111_2$) used in digital clocks and microcontrollers.

Tutorial

How to Use

01
Enter a BCD binary bit sequence (e.g. 0101 1001) or Decimal integer (e.g. 59).
02
Watch both representations sync bidirectionally in real time.
03
Inspect the 4-bit nibble-by-digit mapping table.
04
Review the invalid state detector that flags illegal BCD values ($1010_2$ to $1111_2$).
05
Copy formatted BCD strings formatted with nibble spaces.
Capabilities

Key Features

Standard 8421 BCD Encoding: Translates each decimal digit (0–9) into its distinct 4-bit binary representation.
Pseudo-Tetrade Error Linter: Automatically flags illegal nibbles greater than 9 ($1010_2$ through $1111_2$).
Packed vs Unpacked BCD Support: Toggle between 8-bit 2-digit packed bytes and single-digit unpacked nibbles.
Positional Weights Visualizer: Highlights the 8-4-2-1 power weighting for each 4-bit segment.
Instant Local Execution: Evaluates digital codes in browser memory.
Applications

Common Use Cases

Embedded Systems: Debugging microcontrollers that use BCD for real-time clocks.
Digital Electronics: Working with seven-segment displays and BCD counters.
PLC Programming: Converting industrial sensor data into human-readable formats.
Legacy Computing: Analyzing data from older mainframes and financial systems.
Education: Learning about weighted binary codes and digital logic.
Guidance

Tips & Best Practices

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BCD uses 4 bits to represent each decimal digit (0-9).
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The patterns 1010 through 1111 (10-15) are considered invalid in standard BCD.
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BCD is often used in financial applications where exact decimal representation is required.
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One byte can store two BCD digits (known as "packed BCD").
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Standard BCD is also known as 8421 code based on bit weights.
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Answers

Frequently Asked Questions

Q What is Binary Coded Decimal (BCD) and how does it differ from pure binary?

In pure binary, the entire number is converted to base-2 (e.g. decimal 25 is `11001`). In BCD, each individual decimal digit is encoded separately as a 4-bit binary nibble (e.g. 2 = `0010`, 5 = `0101`, so 25 is `0010 0101`).

Q Why are the binary values 1010 through 1111 invalid in BCD?

Since decimal digits only range from 0 to 9, binary values representing 10 to 15 (1010 to 1111) are unused 'pseudo-tetrades' in 8421 BCD and are flagged as errors.

Q Where is BCD used in electronics and computing?

BCD is widely used in digital clocks, pocket calculators, 7-segment LED displays, financial accounting processors, and industrial PLC controllers to eliminate binary floating-point rounding errors.