What's the most efficient implementation of map(x,0,1023,50,250)?
The screenshot shows a base-2 (i.e. binary) result of calculating the constant part of a mapping. You can approximate this multiplication by a constant by a number of shifts added together. You need to break down each multiplication in the result first:

x * 0.0012 = x >> 3

x * 0.00012 = x >> 4

x * 0.00000012 = x >> 7

Then add these together. You are essentially breaking it down into convenient base-2 multiplies (which can always be represented by shifts) and adds - nearly always more efficient.

This doesn't get you right to 250, but pretty close:

&gt;&gt;&gt; for i in range(0, 1024, 34):
...   print (i &gt;&gt; 3) + (i &gt;&gt; 4) + (i &gt;&gt; 7) + 50
... 
50
56
62
   [snip]
235
241
247
&gt;&gt;&gt; print (1023 &gt;&gt; 3) + (1023 &gt;&gt; 4) + (1023 &gt;&gt; 7) + 50
247


Do all your processing with a left-justified int (ADLAR=1) though, to minimize errors. The ADC returns a 10bit result, and ADLAR choses if this is aligned to the left or right of the two result registers.