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Outbyte Driver Updater FREEFix the driver behind crashes, sound loss and screen glitchesFind Drivers →Outbyte PC Repair FREERepair Windows errors before they cause bigger problemsFix Now →Binary-coded decimal (BCD) represents a decimal number by encoding each decimal digit separately in binary. In the common four-bit form, the decimal number 59 is written as 0101 1001: 0101 represents 5 and 1001 represents 9. This differs from writing 59 as an ordinary binary integer, which is 00111011.
How does binary-coded decimal work?
In natural four-bit BCD, each decimal digit from 0 through 9 has its own four-bit pattern. The bit groups preserve the decimal digits rather than encoding the whole number as one binary integer.
| Decimal digit | Four-bit BCD |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
Example: writing 59 in BCD
- Separate the decimal number into its digits: 5 and 9.
- Encode 5 as
0101and 9 as1001. - Join the groups:
0101 1001.
If those eight bits are interpreted as one ordinary base-two integer, they do not mean decimal 59. In BCD, each four-bit group is read as a decimal digit.
What do the other four-bit patterns mean?
A four-bit group can represent 16 patterns, but the ordinary unsigned BCD digit mapping uses only ten: 0000 through 1001. Patterns 1010 through 1111 are not decimal digits in this mapping. Some formats may assign certain patterns special roles, such as sign codes; their meaning depends on the format.
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What is the difference between packed and unpacked BCD?
“Packed” and “unpacked” describe how digit groups are stored, not a different basic definition of BCD. Intel’s architecture manual describes the following layouts:
| Layout | Storage described by Intel | What it means |
|---|---|---|
| Packed BCD | Two digits per byte | Each half-byte holds one digit; the high half-byte contains the more significant of the two digits. |
| Unpacked BCD | One digit per byte | The low four bits carry the digit value. |
These are layouts documented by Intel, not a claim that every BCD implementation uses identical storage conventions. Intel also describes a specialized 80-bit packed decimal integer format for x87; it is one architecture-specific format, not the definition of BCD as a whole.
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How does signed BCD work?
Signed BCD conventions depend on the format. IBM’s Open XL C/C++ documentation describes BCD built-ins in which digits and a sign field use four bits each, with digits in contiguous arrays and a sign nibble at the end. IBM lists accepted sign-code values and specifies behavior for IBM processor targets. Those details apply to the documented IBM implementation; they are not universal BCD rules.
How does BCD compare with ordinary binary?
BCD keeps decimal digit boundaries directly visible: each four-bit group represents a decimal digit. Ordinary binary instead represents the integer as a whole using binary place values. Straightforward four-bit BCD therefore uses four bits for each decimal digit, while ordinary binary can use its bit patterns to represent the integer directly. The trade-off is digit visibility versus storage density; which representation is preferable depends on the application and implementation.
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Can BCD use less storage than four bits per digit?
Yes. Chen–Ho encoding is a distinct, denser decimal encoding rather than the basic four-bit-per-digit BCD form. IBM Research’s page for M. F. Cowlishaw’s paper Densely packed decimal encoding, published May 1, 2002, describes Chen–Ho as losslessly encoding three BCD digits in 10 bits. The page also notes an improvement that is not limited to groups of three digits. This illustrates that decimal digit information can be retained with less overhead than straightforward BCD, but it should not be confused with the basic BCD definition.
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