BCD Conversion Tool

BCD to Binary Converter

Convert Binary-Coded Decimal (BCD) to ordinary binary instantly. Enter valid 4-bit BCD groups such as 0010 0101, decode the decimal digits, reconstruct the decimal value, and get its exact binary representation.

✓ BCD Validation ✓ Decimal Decoding ✓ Binary Result ✓ Group-by-Group Steps ✓ Free Unlimited Use

BCD→2

BCD → Binary

● Ready

BCD Code

Enter one or more 4-bit BCD groups. Spaces are optional. Valid groups represent decimal digits 0 through 9.

Try:

✓ Binary Result

Ordinary binary representation of the decoded decimal value

Decimal Value 0

BCD Digits 0

Binary Bits 0

BCD Decoding Breakdown

What Is BCD?

BCD stands for Binary-Coded Decimal. Instead of representing an entire number as one ordinary binary value, BCD encodes each decimal digit separately using four bits.

Decimal 25 contains two digits: 2 and 5 Encode each digit separately: 2 → 0010 5 → 0101 Therefore decimal 25 in BCD is: 0010 0101

How to Convert BCD to Binary

1. Split the BCD code

Separate the input into groups of exactly four bits.

2. Decode each group

Convert each 4-bit group into its decimal digit from 0 through 9.

3. Validate each digit

BCD groups representing binary values 10 through 15 are invalid.

4. Join the decimal digits

Place all decoded digits together in their original order.

5. Read the decimal number

The combined digits form the actual numerical decimal value.

6. Convert decimal to binary

Convert that complete base-10 value into ordinary base-2 binary.

BCD Digit Table

Decimal Digit	BCD Code
0	`0000`
1	`0001`
2	`0010`
3	`0011`
4	`0100`
5	`0101`
6	`0110`
7	`0111`
8	`1000`
9	`1001`

Example: Convert BCD 0010 0101 to Binary

BCD input: 0010 0101 Decode each group: 0010 = 2 0101 = 5 Join the decimal digits: 25 Convert decimal 25 to ordinary binary: 25₁₀ = 11001₂ Therefore: 0010 0101 BCD = 11001₂

Example: Convert BCD 0001 0010 0011 to Binary

Decode: 0001 = 1 0010 = 2 0011 = 3 Decimal value: 123 Convert decimal 123 to binary: 123₁₀ = 1111011₂ Therefore: 0001 0010 0011 BCD = 1111011₂

BCD Is Not the Same as Ordinary Binary

This is one of the most important points when working with Binary-Coded Decimal. A BCD bit string must be interpreted in groups of four, while ordinary binary represents the complete numerical value with one continuous sequence.

Decimal 25 as BCD: 0010 0101 Decimal 25 as ordinary binary: 11001 These are different encodings of the same numerical value.

Why Does BCD Use Four Bits Per Decimal Digit?

A decimal digit can have ten possible values, from 0 through 9. Four binary bits can represent sixteen different patterns, which is enough to encode all ten digits.

Standard 8421 BCD therefore assigns one four-bit group to every decimal digit.

Invalid BCD Codes

Four bits can represent values from 0 through 15, but a decimal digit can only range from 0 through 9. Therefore six possible four-bit combinations are invalid in standard BCD.

Invalid BCD digit groups: 1010 1011 1100 1101 1110 1111 These correspond to binary values 10 through 15 and cannot represent one decimal digit.

BCD to Binary Examples

BCD	Decimal	Ordinary Binary
`0000`	0	`0`
`0001`	1	`1`
`0101`	5	`101`
`1001`	9	`1001`
`0001 0000`	10	`1010`
`0001 0001`	11	`1011`
`0010 0101`	25	`11001`
`1001 1001`	99	`1100011`
`0001 0010 0011`	123	`1111011`

BCD vs Excess-3

Feature	BCD	Excess-3
Bits per decimal digit	4	4
Encoding method	Direct digit value	Digit + 3
Code for digit 0	`0000`	`0011`
Code for digit 5	`0101`	`1000`
Code for digit 9	`1001`	`1100`

Does Spacing Matter?

No. This calculator removes spaces before processing the BCD input. You can therefore enter the groups separately or as one continuous bit string.

Both inputs are equivalent: 0010 0101 00100101 Both decode to decimal 25 and ordinary binary 11001.

What About Leading Zeros?

Leading BCD zero digits can be decoded correctly, but they do not change the final numerical value.

BCD: 0000 0010 0101 Decoded decimal digits: 025 Numerical value: 25 Ordinary binary: 11001

Where Is BCD Used?

BCD has historically been useful in systems where decimal digits must be represented or displayed directly, including calculators, financial systems, digital clocks, meters, displays, and some embedded electronics.

It makes decimal digit handling straightforward, although it generally uses more bits than ordinary binary for the same numerical value.

Common BCD to Binary Mistakes

Reading all bits as ordinary binary

BCD must first be split into four-bit decimal digit groups.

Accepting values 10–15

Groups from 1010 through 1111 are invalid standard BCD digits.

Using incomplete groups

The total number of BCD bits must be divisible by four.

Confusing BCD with Excess-3

BCD directly encodes each decimal digit, while Excess-3 adds 3 before encoding.

Important: this calculator uses standard unsigned 8421 BCD. Signed BCD, packed decimal formats, and fractional BCD may require additional formatting rules.

Related BinaryCon Tools

BCD to Binary Converter FAQs

How do you convert BCD to binary?

Decode each four-bit BCD group into its decimal digit, combine the digits into the full decimal number, and then convert that decimal value to ordinary binary.

What is BCD 0101 in binary?

BCD 0101 represents decimal digit 5. Decimal 5 is ordinary binary 101.

What is BCD 0010 0101 in binary?

The groups decode to decimal digits 2 and 5, giving decimal 25. Decimal 25 is binary 11001.

What is BCD 0001 0000 in binary?

The BCD groups decode to decimal 10, which is ordinary binary 1010.

What is BCD 1001 1001 in binary?

The BCD code represents decimal 99, which equals binary 1100011.

Is BCD the same as binary?

No. BCD encodes every decimal digit separately using four bits, while ordinary binary encodes the complete numeric value directly in base 2.

Why are 1010 through 1111 invalid BCD digits?

Those groups represent binary values 10 through 15, but a single decimal digit can only have a value from 0 through 9.

Can BCD contain spaces?

Yes. Spaces between four-bit groups are optional and are ignored by the calculator.

Does the BCD input need a multiple of four bits?

Yes. Every BCD decimal digit occupies exactly four bits, so the total number of bits must be divisible by four.

Is BCD the same as Excess-3?

No. BCD directly encodes decimal digits, while Excess-3 adds 3 to each decimal digit before creating the four-bit code.

Can this converter process large BCD values?

Yes. The decoded decimal value is processed using integer arithmetic rather than ordinary floating-point numbers.

Does BinaryCon require registration?

No. The BCD to Binary Converter can be used directly without signup.