About

Binary Coded Decimal (BCD) encodes each decimal digit as a separate 4-bit binary nibble. Converting BCD to octal requires an intermediate decimal stage: each nibble is decoded to its decimal digit (valid range 0000 - 1001), the digits are concatenated into a full decimal integer, and that integer is then divided repeatedly by 8 to produce the octal representation. A single invalid nibble (value ≥ 10) renders the entire BCD string malformed. This tool performs that two-stage conversion with full validation, rejecting pseudo-tetrades and flagging the exact nibble position of any error. It also operates in reverse - octal to BCD - for verification workflows in embedded systems and legacy mainframe data recovery.

Misinterpreting packed BCD data as straight binary is a common source of off-by-magnitude errors in COBOL migration, PLC register reads, and financial record parsing. The tool assumes unsigned, integer-only BCD (no sign nibble, no fractional digits). For packed BCD with sign nibbles (1100 positive, 1101 negative), strip the trailing nibble before conversion.

Formulas

The conversion proceeds in two deterministic stages. First, the BCD binary string is segmented into 4-bit nibbles from the least significant bit. Each nibble N_i is decoded to its decimal value:

d_i = N_i[3] × 8 + N_i[2] × 4 + N_i[1] × 2 + N_i[0]

A validity constraint is enforced: d_i ≤ 9. Any nibble producing a value ≥ 10 is a pseudo-tetrade and rejected. The full decimal value is then reconstructed:

D = n−1∑i=0 d_i × 10ⁱ

Second, the decimal integer D is converted to octal by repeated division:

D = q × 8 + r, where r = D mod 8

Remainders r are collected in reverse order until q = 0.

Where N_i = the i-th 4-bit BCD nibble (right to left), d_i = decoded decimal digit, D = full decimal integer, n = number of nibbles, q = quotient, r = remainder.

Reference Data

Decimal Digit	BCD Nibble	Octal (of digit)	Valid BCD?
0	0000	0	Yes
1	0001	1	Yes
2	0010	2	Yes
3	0011	3	Yes
4	0100	4	Yes
5	0101	5	Yes
6	0110	6	Yes
7	0111	7	Yes
8	1000	10	Yes
9	1001	11	Yes
10	1010	-	No (pseudo-tetrade)
11	1011	-	No (pseudo-tetrade)
12	1100	-	No (pseudo-tetrade)
13	1101	-	No (pseudo-tetrade)
14	1110	-	No (pseudo-tetrade)
15	1111	-	No (pseudo-tetrade)
Common Multi-Digit Examples
42	0100 0010	52	Yes
99	1001 1001	143	Yes
128	0001 0010 1000	200	Yes
255	0010 0101 0101	377	Yes
1000	0001 0000 0000 0000	1750	Yes
4096	0100 0000 1001 0110	10000	Yes
9999	1001 1001 1001 1001	23417	Yes
65535	0110 0101 0101 0011 0101	177777	Yes

Frequently Asked Questions

Nibble values from 1010 (10) through 1111 (15) are called pseudo-tetrades. They have no valid decimal mapping in 8421 BCD. The converter rejects the entire input and reports which nibble is invalid. This is not a recoverable error - the source data is either corrupted or uses a non-8421 encoding (e.g., Excess-3, Aiken code).

The converter pads the leftmost (most significant) group with leading zeros. For example, an input of 110010 (6 bits) is treated as 0011 0010, decoding to decimal 32, then octal 40. This matches the standard convention for BCD nibble alignment.

No. Packed BCD formats (common in COBOL and IBM mainframes) append a sign nibble: 1100 for positive, 1101 for negative. This converter treats all nibbles as data. Strip the trailing sign nibble before pasting, then manually apply the sign to the octal result.

JavaScript handles integers exactly up to 2⁵³ − 1 (9007199254740991). This corresponds to a BCD string of up to 64 bits (16 nibbles). For values beyond this, the converter uses BigInt arithmetic internally, supporting arbitrarily large BCD strings without precision loss.

Octal was historically used in PDP-series minicomputers and early Unix systems where word sizes were multiples of 3 bits. BCD data from financial peripherals (card readers, banking terminals) often needed translation to octal for register-level debugging. Today it remains relevant when reading legacy core dumps or PLC memory maps formatted in octal.

No. BCD and octal represent numbers via fundamentally different grouping: BCD uses 4-bit groups mapped to decimal digits 0 - 9, while octal uses 3-bit groups mapped to digits 0 - 7. The numeric value is preserved, but the underlying bit pattern changes entirely. For example, BCD 0001 0010 (decimal 12) becomes octal 14 (binary 001 100).