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Category Unit Converters

BCD Input (binary digits) Enter 4-bit nibbles (0 and 1 only). Spaces allowed for readability.

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About

Binary Coded Decimal (BCD) encodes each decimal digit 0 - 9 as a fixed 4-bit binary nibble. The valid range per nibble is 0000₂ through 1001₂. Nibbles from 1010 to 1111 are illegal in BCD and indicate corrupted or misinterpreted data. Misreading a BCD stream as straight binary produces a different numeric value entirely - a common source of bugs in legacy PLC systems, BIOS clocks, and financial hardware that still rely on BCD encoding. This tool validates every nibble, reconstructs the decimal integer, then performs repeated division by 8 to produce the octal representation. It handles arbitrarily large BCD strings via BigInt arithmetic, so precision is not lost even for 64-digit inputs. Note: the converter assumes unsigned, packed BCD (no sign nibble).

Formulas

The conversion proceeds in two stages. First, BCD nibbles are decoded to a decimal integer. Second, that integer is converted to octal via repeated division.

Stage 1 - BCD to Decimal:

Given n nibbles N₀, N₁, … N_n−1 (each a 4-bit value where 0 ≤ N_i ≤ 9):

D = n−1∑i=0 N_i × 10^(n−1−i)

Stage 2 - Decimal to Octal:

Repeatedly divide D by 8, collecting remainders r_k:

D = 8 × Q + r, where 0 ≤ r < 8

The octal digits are the remainders read in reverse order (last remainder is the most significant digit).

Where D = decimal integer, N_i = value of the i-th BCD nibble, Q = quotient, r = remainder, n = total number of nibbles.

Reference Data

Decimal Digit	BCD Nibble	Octal Equivalent	Binary (Straight)
0	0000	0	000
1	0001	1	001
2	0010	2	010
3	0011	3	011
4	0100	4	100
5	0101	5	101
6	0110	6	110
7	0111	7	111
8	1000	10	1000
9	1001	11	1001
Invalid BCD Nibbles (not used)
10 (invalid)	1010	-	1010
11 (invalid)	1011	-	1011
12 (invalid)	1100	-	1100
13 (invalid)	1101	-	1101
14 (invalid)	1110	-	1110
15 (invalid)	1111	-	1111
Multi-digit BCD Examples
42	0100 0010	52	101010
99	1001 1001	143	1100011
128	0001 0010 1000	200	10000000
255	0010 0101 0101	377	11111111
1000	0001 0000 0000 0000	1750	1111101000
4096	0100 0000 1001 0110	10000	1000000000000
9999	1001 1001 1001 1001	23417	10011100001111
65535	0110 0101 0101 0011 0101	177777	1111111111111111

Frequently Asked Questions

Nibbles from 1010 (10) through 1111 (15) are invalid in standard 8421 BCD. This converter flags each invalid nibble and refuses to produce a result until corrected. In hardware, such codes sometimes represent sign indicators or error states, but in packed unsigned BCD they are always illegal.

Yes. If the total bit count is not divisible by 4, the converter left-pads the input with leading zeros to complete the most significant nibble. For example, 110 becomes 0110, which decodes to decimal 6.

BCD is not a positional binary encoding. The decimal value 99 in BCD is 1001 1001 (8 bits), but in straight binary it is 1100011 (7 bits). Octal groups bits in threes from the binary equivalent, which is useful in legacy systems (PDP, UNIX file permissions). Converting through decimal ensures correctness because BCD encodes decimal digits, not binary magnitudes.

The converter uses JavaScript BigInt arithmetic internally, so it handles arbitrarily large BCD strings without precision loss. Inputs exceeding 1000 nibbles (4000 bits) may cause slight UI delay but will still produce correct results.

Standard BCD (8421 weighting) maps digit d directly to its 4-bit binary form. Excess-3 adds 3 to each digit before encoding (so 0 becomes 0011). Gray BCD uses reflected Gray code per nibble. This tool assumes 8421 BCD exclusively. Feeding Excess-3 data will produce incorrect results unless you subtract 3 from each nibble first.

Yes. The converter strips all whitespace and non-binary characters before processing. You can enter 0100 0010 or 01000010 interchangeably. Nibble-separated input is recommended for readability.