2007/2/19, Dick Moores <[EMAIL PROTECTED]>:
At 02:17 AM 2/19/2007, Andre Engels wrote: >To understand these operators, you will have to think of the numbers >as binary numbers. Look at the digits. For two numbers x and y, x^y >is the effect of doing an exclusive or on all digits (that is, 0^1 = >1^0 = 1 and 0^0 = 1^1 = 0), & of doing an and (1&1 = 1, >1&0=0&1=0&0=0) and | is an or on all digits (1|1=1|0=0|1 = 1, 0|0 = 0). > >So 5^8 = 110 ^ 1000 = 0110 ^ 1000 = 1110 = 13 >and 13^8 = 1110 ^ 1000 = 0110 = 5 Thanks, Andre! I've got it for the three operators, for non-negative integers. But I'm not sure I understand how negative integers work. For example, is 3 & -3 = 1 because it is 11 & -11 = 01, and that's because one of the first digits of 11 and -11 is not 1, and both of their 2nd digits ARE 1, Q.E.D.?
This has to do with the internal representation of negative numbers: -1 is represented as 111....111, with one 1 more than maxint. -2 is 111...110 and -3 is 111...101. Thus 3 & -3 is 11 & 111...101 = 1 Also, of what practical use are these things?
I guess they have their uses for people accustomed to dealing with hardware. Apart from that, you can get a very space-efficient representation for multiple boolean variables. If you have what looks like an array of booleans, you could also represent it as a single natural number, for example [true, true, false, false, true, false] would then be 1*1 + 1*2 + 0*4 + 0*8 + 1*16 + 0*32 = 19. Using such a representation and the above operators would enable one to write z = x & y instead of z = [x[i] and y[i] for i in range(len(x))] when modelling the same using lists. Of course this does come at the price of complicating x[i] = true to x |= 2 ** i which though not really longer does definitely look harder to understand. -- Andre Engels, [EMAIL PROTECTED] ICQ: 6260644 -- Skype: a_engels
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