An efficient algorithm for converting ASCII hex to binary
Ken Sykes (72177,141)
David Ogle (75676,2612)

    There is a well-known algorithm for converting a binary number between
one and fifteen to its equivalent hex form in ASCII that only requires
four assembly language instructions.  Assuming that the number to convert is 
in AL, the following sequence performs the conversion:

		add	al,90h
		daa
		adc	al,40h
		daa

    This instruction sequence is, as far as we know, the shortest (16 cycles)
self-contained routine to convert a binary number to hex.  Inspired by
this code and the fact that a similar routine to convert ASCII hex to
binary would be useful, we came up with two algorithms that convert an
ASCII hex digit to binary in five assembly instructions or less.

    The first algorithm takes advantage of an undocumented feature of the
8088.  The AAM instruction (Ascii Adjust for Multiply) divides AL by 10,
placing the remainder in AL and the quotient in AH.  The opcode for
AAM is:	0D4h,0Ah.  It's no coincidence that the second byte is 10 - the 
8088 uses the second byte of the opcode as the divisor!  The same rule
applies to the AAD (Ascii Adjust for Division) instruction.  With this in 
mind, a conversion routine goes as follows (assuming the ASCII digit is in 
AL and in the range '0..9,A..F'):

		sub	al,'0'
		aam	16
		aad	9

    The only problem is the Microsoft Assembler does not accept this form.
By placing the opcodes in data statements, however, the following code 
will assemble properly:

		sub	al,'0'
		db	0D4h,10h
		db	0D5h,09h

    At three instructions and six bytes of code space, We are reasonably
sure this is the shortest self-contained sequence to perform the conversion.
The only drawbacks are the use of non-standard opcodes and the execution
time (147 cycles!).  The second algorithm, loosely-based on this one, 
relieves these restrictions.

    The second algorithm makes exclusive use of fast instructions to
perform the conversion (again, AL holds the digit to convert):

		add	al,40h
		cbw
		and	ah,09h
		add	al,ah
		and	al,0Fh

    While two additional instructions are required, the routine executes 
in 17 cycles.  We are reasonably sure this is the fastest-executing self-
contained code to perform the conversion. It has the added benefit of 
handling the ASCII values 'a'..'f'.

    These algorithms will hopefully trim down the execution times of your
programs, and we welcome any suggestions or improvements on our code.

Happy Hacking!




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