Published in EPE Dec '03 issue. By PETER HEMSLEY
Speed up your PIC's data conversion and compression.
Here are the first five powers of ten:
1 = 1 10 = 8 + 2 100 = 64 + 32 + 4 1000 = 512 + 256 + 128 + 64 + 32 + 8 10000 = 8192 + 1024 + 512 + 256 + 16If X represents any decimal digit between 0 and 9 then:
X = (X * 1) X0 = (X * 8) + (X * 2) X00 = (X * 64) + (X * 32) + (X * 4) X000 = (X * 512) + (X * 256) + (X * 128) + (X * 64) + (X * 32) + (X * 8) X0000 = (X * 8192) + (X * 1024) + (X * 512) + (X * 256) + (X * 16)These five expressions are the basis on which we can write a routine to convert a string of decimal digits into binary. The routine is to be written in assembler so any expression must be conducive to available processor instructions, namely NIBBLE SWAP, SHIFT LEFT and ADD.
Conducive numbers to work with are:
2 (SHIFT LEFT to multiply by 2) 16 (NIBBLE SWAP to multiply by 16) 256 (The result goes into the high byte of the binary)If your mind is somewhat blank at this point let's try a simple example to get the grey matter working.
The number 300 can be written as:
(3 * 64) + (3 * 32) + (3 * 4)Rewriting it in terms of conducive numbers we get:
3 * 16 * 2 * 2 + 3 * 16 * 2 + 3 * 2 * 2Now reduce and rearrange the expression to:
((3 * 16 + 3) * 2 + 3 * 16) * 2 = 300Check it with your calculator.
This expression can be calculated easily using NIBBLE SWAP, SHIFT LEFT and ADD.
Ok that was easy enough, so now for the tricky part.
The 1000's and 10000's expressions contain six and five terms respectively. If we also use SUBTRACT, the number of terms can be reduced to three and four:
X = (X * 1) X0 = (X * 8) + (X * 2) X00 = (X * 64) + (X * 32) + (X * 4) X000 = (X * 1024)  (X * 32) + (X * 8) X0000 = (X * 8192) + (X * 2048)  (X * 256) + (X * 16)These five expressions can now be written in terms of conducive numbers and combined to give:
N = (((D1 + D3 + D4 * 256) * 2 + D2 * 16 + D2 + D3 * 256) * 2  D3 * 16 + D2 * 16 + D1 + D4 * 16 * 256) * 2 + D4 * 16 + D0  D4 * 256Where D0 = ones, D1 = tens, D2 = hundreds, D3 = thousands, D4 = ten thousands
To save a lot of typing, and you a big headache, the details of how this expression was arrived at have been omitted. It is simple enough though a little lengthy.
There is a problem however, it is the D4 * 256 at the end of the expression. If the input is greater than 63231 the running total will exceed the allotted 16 bits. So, again, rearrange the expression.
N = (((D1 + D3 + D4 * 256) * 2 + D2 * 16 + D2 + D3 * 256) * 2  D3 * 16 + D2 * 16 + D1) * 2 + D4 * 16 + D0  D4 * 256 + D4 * 16 * 256 * 2Now there is an addition of a large number at the end of the expression, therefore overflow will not occur.
The PIC routine in Listing 1 is an almost literal translation of this expression into assembler, with just a few tweaks to make the code more efficient. The variables may be allocated (equated) to any registers of your choice.
Incidentally, the routine will work with numbers up to 99999, the 17th bit (or bit 16) being returned in the carry.
Finally, if your numerical value is expressed in ASCII characters, each character may be converted to a BCD (binarycodeddecimal) format by subtracting 48, which makes it easy to then check if it is a valid decimal digit.
[xh]RESOURCE This software routine is available from the [i]EPE PCB Service[r] on 3.5in disk (Disk 6, [i]PIC Tricks[r] folder), for which a nominal handling charge applies. It is also available for free download from the [i]EPE[r] Downloads page, accessible via the home page at [bo]www.epemag.wimborne.co.uk[r]. It is in the [i]PIC Tricks[r] folder, as file [bo]Dec2Bin16.txt[r].
Code:
LISTING 1 ; 5 digit decimal to 16 (17) bit binary. By Peter Hemsley, March 2003. ; Input decimal digits in D0 (LSD) to D4 (MSD) ; Output 16 bit binary in NUMHI and NUMLO ; No temporary variables required ; Code size: 33 instructions ; Execution time: 33 cycles (excluding Call and Return) ; Returns carry set if > 65535 (and NUMHILO MOD 65536) dec2bin16 movf D1,W ; (D1 + D3) * 2 addwf D3,W movwf NUMLO rlf NUMLO,F swapf D2,W ; + D2 * 16 + D2 addwf D2,W addwf NUMLO,F rlf D4,W ; + (D4 * 2 + D3) * 256 addwf D3,W movwf NUMHI rlf NUMLO,F ; * 2 rlf NUMHI,F swapf D3,W ;  D3 * 16 subwf NUMLO,F skpc decf NUMHI,F swapf D2,W ; + D2 * 16 + D1 addwf D1,W addwf NUMLO,F skpnc incf NUMHI,F swapf D4,W ; + D4 * 16 + D0 addwf D0,W rlf NUMLO,F ; * 2 rlf NUMHI,F addwf NUMLO,F skpnc incf NUMHI,F movf D4,W ;  D4 * 256 subwf NUMHI,F swapf D4,W ; + D4 * 16 * 256 * 2 addwf NUMHI,F addwf NUMHI,F return ; Q.E.D.+
Comments:
/techref/microchip/math/radix/bu2b5d16bph.htm This was what I was looking for, an efficient BCD to binary conversion. I download data from a PC that was manipulated by EXCEL onto a PIC for storage on an external EEPROM. This conversion was required to generate proper address bytes for the memory EEPROMs.+
I do have one request, is it possible to expand this logic to support the 17bit addressing of the 128KB AT24C1024 Serial EEPROM?
I'm not quite capable of expanding the code myself. I can follow your explanation, but my math skills end about there. An expanded version capable of supporting a number of 131,072 would be greatly appreciated.
Thank you very much for the current version!
Robert Hedan
:)
Questions:
There seem to be an error in the code. The lines "D2*16+D1 +D4*16+D0 *2" should be "D2*16+D1 *2 +D4*16+D0"+
This way the program goes OK in my simulator.
Am I correct?
See also:
file: /Techref/microchip/math/radix/bu2b5d16bph.htm, 7KB, , updated: 2007/7/7 22:07, local time: 2018/4/23 14:12,
owner: JMNEFP786,

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