66 lines
1.7 KiB
Markdown
66 lines
1.7 KiB
Markdown
# Print 16-bit Fixed Point Fraction
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# Theory
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Printing the fractional value of a 16-bit fixed point number in decimal is rather trivial.
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For example, the number `0.7106` in 16-bit fixed point is 0.71506 * 65536 = 46,569 = `$B5E9`
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* Q. How do we convert the number `$B5E9` back into `.7106` ?
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* Q. By _digit peeling._
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Given a fractional number `N` represented as a 16-bit integer then the pseudo-code is:
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1. Multiply N by 10
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2. Print the Integer Part of `N` (a digit)
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3. Set the Integer Part to zero
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5. Have we printed the total number of decimal digits we want? If no then goto step 1
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Example:
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```
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+-----------------------------+
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0.7106 * 65536 = $B5E9 |
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v '.'
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$B5E9 * $A = $7.1B1A
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$1B1A * $A = $1.0F04
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$0F04 * $A = $0.9628
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$9628 * $A = $5.DD90
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$5DD9 * $A = $8.A7A0
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```
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An optimization for `N*10` is that this is equivalent to: `N*8 + N*2`
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# Application
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## Assembly (Source)
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See file [print_fract.s](print_fract.s)
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## Binary (Executable)
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```
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CALL-151
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0800:a2 b5 a0 e9 20 1a 08 a9 ae 20 ed fd a2 00 bd 76
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0810:08 20 ed fd e8 e0 05 d0 f5 60 8e 71 08 8c 72 08
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0820:20 6a 08 aa 20 60 08 20 54 08 20 60 08 20 60 08
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0830:20 44 08 ad 70 08 09 b0 9d 76 08 20 6a 08 e8 e0
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0840:05 d0 e1 60 18 a0 02 b9 70 08 79 73 08 99 70 08
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0850:88 10 f4 60 a0 02 b9 70 08 99 73 08 88 10 f7 60
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0860:0e 72 08 2e 71 08 2e 70 08 60 a9 00 8d 70 08 60
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0870:00 00 00 00 00 00 00 00 00 00 00
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800G
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E000G
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```
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## Output
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```
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.71058
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```
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