Kerry Wentworth wrote:
> Actually, a full scale A/D reading in left justified 10.6 format is
> 1111111111.000000, in binary, 0000001111111111, or decimal 1023.
> For a half scale reading (i.e. 2.5V on a 5V reference) would be either
> 1000000000.000000 or 0111111111.000000, in binary 0000001000000000 or
> 0000000111111111, or decimal 511 or 512.  When you read the A/D result
> registers in a PIC, you can choose which format you get.
>
> In 10.6 math, there is an imaginary decimal point between bits 5 and
> 6. Bit 6 has a value of 1, bit 7 is 2, bit 8 is 4, etc.
> Bit 5 would have a value of 1/2, bit 4 is 1/4, bit 3 is 1/8, bit 2 is
> 1/16, bit 1 is 1/32 and bit 0 is 1/64.
>
> Now let's say we are implementing Olin's filter, and want to multiply
> our A/D reading by 1/16.
> 1/16 has bit 4 set, and all others cleared, so it is
> 0000000000.000100, which is a binary 4.
> when we multiply 0111111111.000000 by 0000000000.000100 we get
> 0000 0000 0000 0001 1111.1111 0000 0000, which is too large to fit
> into 16 bits, and so becomes a 32 bit bit number, in 20.12 format.
> But the last 6 bits will always be 0, so we don't really need them.
> Without them, the number would fit into 16 bits, and in fact would
> fit into the
> 10.6 format.  We could do that by right shifting 6 times and taking
> the lowest 16 bits.  We would end up with 0000 0111 11.11 1100.  The
> end result off all of this is that we took a number, multiplied it by
> 4 then divided it by 64.
>
> Reading the A/D in right justified mode results in a number that is
> already right shifted by 6 bits (i.e. divided by 64), so taking our
> reading as 0000000111111111 and multiplying by 0000000000000100 would
> give us
> 0000 0111 11.11 1100, which will fit into a 16 bit number without
> overflow, and is in fact in 10.6 format, with the fractional bits
> right where they oughta be, without ever needing a 32 bit variable.

Did I miss a point you were trying to make somewhere in there, a question,
or are you just saying out loud what you think you understand to try to mak=
e
more sense of it?


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