Intel BCD opcode


The Intel BCD opcodes are a set of x86 instructions that operate with binary coded decimal numbers.
The radix used for the representation of numbers in the x86 processors is 2.
This is called a binary numeral system.
However the x86 processors do have limited support for the decimal numeral system.
BCD instructions are no longer supported in long mode.

Usage

Number representation

BCD numbers can be represented in two ways: packed decimal and unpacked decimal.
Only the decimal numbers 0 to 99 can be added directly.
First the numbers are added as usual using add. The processor will set the adjust flag if the sum of both lower nibbles is 16 or higher, and the carry flag if the sum of both bytes is 256 or higher.
Then the result is adjusted, depending on the number representation.
Only the decimal numbers 0 to 99 can be subtracted directly.
First the numbers are subtracted as usual using sub. The processor will set the adjust flag if a borrow occurred in the least significant nibble, and the carry flag if a borrow occurred in the most significant nibble.
Only unpacked representation is supported. Only two single digit numbers can be multiplied.
First the digits are multiplied as usual using mul.
Then the result is adjusted using aam : The processor divides the result by ten, storing the quotient in the most significant byte of the result and the remainder in the least significant byte of the result.

Division

Only unpacked representation is supported.
Operands must fall in the range 0 to 99.
First the operands are converted to normal binary representation using aad : The processor converts numbers by multiplying the most significant byte by 10 and adding the least significant byte. The quotient and remainder of the division are obtained as usual using div, and will be present in normal binary representation.

Application

numbers are used for storing decimal numbers, especially in financial software.
The opcodes mentioned above give the x86 rudimentary BCD support.

Alternatives

Adding BCD numbers using these opcodes is a complex task, and requires many instructions to add even modest numbers. It can also require a large amount of memory. If only doing integer calculations, then all integer calculations are exact, so the radix of the number representation is not important for accuracy. On an x86 processor, calculations with binary numbers are usually a lot faster than the same calculations with BCD numbers.