# SXMicrocontrollerMathMethod

## Scale 8 bits to a percent

;*******************************************************************

```;scale_hex2dec
;  The purpose of this routine is to scale a hexadecimal byte to a
;decimal byte. In other words, if 'h' is a hexadecimal byte then
;the scaled decimal equivalent 'd' is:
;    d = h * 100/256.
;Note that this can be simplified:
;    d = h * 25 / 64 = h * 0x19 / 0x40
;Multiplication and division can be expressed in terms of shift lefts
;and shift rights:
;    d = [ (h<<4) + (h<<3) + h ] >> 6
;The program divides the shifting as follows so that carries are
automatically
;taken care of:
;    d =   (h + (h + (h>>3)) >> 1) >> 2
;
;Inputs:   W - should contain 'h', the hexadecimal value to be scaled
;Outputs:  W - The scaled hexadecimal value is returned in W
;Memory:   temp
;Calls:    none

scale_hex2dec

mov	temp, W	;Hex value is in W.
clrb	C	;Clear the Carry bit so it doesn't affect RRF

;Nikolai Golovchenko says: For better precision (especially for higher
;values of input byte), one more term should be added, so that
;d  = (((h >> 3 + h) >> 3 + h) >> 1 + h) >> 2 = h * (1/4 + 1/8 + 1/64 + 1/512)
;
;This adds only 6 cycles, and reduces errors from 51 to 11 cases per
;all combinations of input (in both routines absolute errors are small,+-1).
;
;	rr	temp
;	clrb	C
;	rr	temp
;	clrb	C
;	rr	temp

rr	temp
clrb	C
rr	temp
clrb	C
rr	temp	;temp = h>>3
add	temp, W	;temp = h + (h>>3)
rr	temp	;temp = (h + (h>>3)) >> 1
add	temp, W	;temp = h + ((h + (h>>3)) >> 1)
rr	temp
clrb	C
mov	W, >>temp	;d = W = (h + (h + (h>>3)) >> 1) >> 2

ret

```

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