BCD Decoder

BCD to Decimal Converter

Convert Binary-Coded Decimal (BCD) directly to decimal. Enter valid 4-bit BCD groups such as 0010 0101 to decode every decimal digit, validate the BCD input, and reconstruct the complete base-10 number instantly.

✓ 8421 BCD ✓ Decimal Output ✓ Invalid Code Detection ✓ Digit Breakdown ✓ Free Unlimited Use

BCD→10

BCD → Decimal

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BCD Code

Enter complete 4-bit BCD groups. Spaces are optional. Valid groups range from 0000 through 1001.

Try:

✓ Decimal Result

Decimal value decoded from Binary-Coded Decimal

BCD Groups 0

Input Bits 0

Decimal Digits 0

BCD Decoding Breakdown

What Is BCD to Decimal Conversion?

BCD to decimal conversion decodes Binary-Coded Decimal into ordinary base-10 digits. In standard 8421 BCD, every decimal digit is represented independently by a four-bit binary group.

BCD: 0010 0101 Decode each group: 0010 = 2 0101 = 5 Join the digits: 25 Therefore: 0010 0101 BCD = 25₁₀

How to Convert BCD to Decimal

1. Split into 4-bit groups

Every BCD decimal digit must contain exactly four bits.

2. Read each group as binary

Convert each four-bit group into its unsigned value.

3. Check for valid BCD

The group value must be between decimal 0 and 9.

4. Record each decimal digit

Every valid BCD group maps directly to one decimal digit.

5. Keep the original order

Do not add the decoded digits together.

6. Join the digits

The sequence of decoded digits forms the decimal number.

Standard BCD Code Table

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

Example: BCD 0010 0101 to Decimal

Input: 0010 0101 First group: 0010₂ = 2 Second group: 0101₂ = 5 Combine the digits: 25 Final result: 0010 0101 BCD = 25 Decimal

Example: BCD 0001 0010 0011 to Decimal

Decode each group: 0001 = 1 0010 = 2 0011 = 3 Keep the digits in order: 1 2 3 Therefore: 0001 0010 0011 BCD = 123 Decimal

Why Don’t You Add the Decoded BCD Digits?

Each BCD group represents one position in the decimal numeral. The groups are not independent values that should be summed.

BCD: 0010 0101 means: digit 2 followed by digit 5 Therefore the answer is: 25 not: 2 + 5 = 7

Invalid BCD Groups

Four bits can represent values from 0 through 15. Standard 8421 BCD only uses the first ten values because a decimal digit ranges only from 0 through 9.

Invalid BCD groups: 1010 = 10 1011 = 11 1100 = 12 1101 = 13 1110 = 14 1111 = 15 None of these can represent a single decimal digit in standard BCD.

BCD to Decimal Examples

BCD	Decimal
`0000`	0
`0101`	5
`1001`	9
`0001 0000`	10
`0001 0001`	11
`0010 0101`	25
`0100 0010`	42
`1001 1001`	99
`0001 0010 0011`	123

BCD vs Ordinary Binary

Feature	BCD	Ordinary Binary
Encoding unit	Each decimal digit	Whole numeric value
Bits for decimal 25	`0010 0101`	`11001`
Decimal-friendly	Yes	Not digit-by-digit
Storage efficiency	Lower	Generally higher

BCD vs Excess-3

BCD and Excess-3 both encode decimal digits using four-bit groups, but their digit mappings are different.

Decimal digit 5: BCD = 0101 Excess-3 = 1000 Standard BCD directly represents the digit. Excess-3 first adds 3.

Can BCD Contain Leading Zeros?

Yes. Leading decimal zeros can be represented using the BCD group 0000.

0000 0001 0010 decodes digit-by-digit as: 012 Numerically, that is decimal 12.

The calculator displays the decoded digit sequence so leading BCD zeros remain visible in the conversion breakdown.

Does Spacing Matter?

No. Spaces are removed before validation, so both grouped and continuous BCD inputs are accepted.

These are equivalent: 0010 0101 00100101 Both represent decimal 25.

Common BCD to Decimal Mistakes

Reading the entire string as binary

BCD must be decoded in independent four-bit groups.

Adding decoded digits

BCD digits are concatenated in order rather than added together.

Accepting invalid groups

Standard BCD groups above 1001 are invalid.

Using incomplete groups

The total input length must be divisible by four bits.

Important: this calculator uses standard unsigned 8421 Binary-Coded Decimal. Other BCD variants, signed packed decimal formats, or fractional encodings can follow additional rules.

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BCD to Decimal Converter FAQs

How do you convert BCD to decimal?

Split the BCD input into four-bit groups, decode each group as a decimal digit from 0 through 9, and join those digits in the same order.

What is BCD 0101 in decimal?

0101 is decimal digit 5, so the answer is 5.

What is BCD 0010 0101 in decimal?

0010 represents digit 2 and 0101 represents digit 5, so the decimal number is 25.

What is BCD 0001 0000 in decimal?

The groups represent decimal digits 1 and 0, giving decimal 10.

What is BCD 1001 1001 in decimal?

Each 1001 represents digit 9, so the result is decimal 99.

Is 1010 valid BCD?

No. Binary 1010 equals decimal 10, which cannot fit into one decimal digit.

What BCD groups are invalid?

Standard BCD does not use 1010, 1011, 1100, 1101, 1110, or 1111.

Does every BCD digit use four bits?

Yes. Standard 8421 BCD uses exactly four bits for each decimal digit.

Is BCD the same as ordinary binary?

No. BCD encodes individual decimal digits, while ordinary binary represents the entire number directly in base 2.

Can I enter BCD without spaces?

Yes. Spaces are optional as long as the total number of bits forms complete four-bit groups.

Can BCD represent leading decimal zeros?

Yes. Decimal zero is encoded as 0000, so leading zero digits can be preserved.

Does BinaryCon require registration?

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