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Proceed to Safety

Bitwise Parallel Computation with Block Fill and Copy  

The Sixteen Two-Argument Boolean Functions

+--------------------------------------------------+ A 0011


B 0101   Description


0000 0 (always false)   (0-argument function)


0001 A & B


0010 A & ~B


0011 ~A   (not A)   (1-argument function)


0100 ~A & B


0101 B   (1-argument function)


0110 A ^ B   (A xor B)


0111 A | B   (A or B)


1000 ~(A | B)   (A nor B)


1001 ~(A ^ B)   (A xnor B)


1010 ~B   (not B)   (1-argument function)


1011 ~A | B   (A implies B)


1100 ~A   (not A)   (1-argument function)


1101 A | ~B   (B implies A)


1110 ~(A & B)   (A nand B)


1111 1 (always true)   (0-argument function)

+-------------------------------------------------------+

Primitives

Data can be copied without modification with /clone using the most simple options.

Negation can be achieved in-place using a sequence of three /fill commands:

/fill x1 y1 z1 x2 y2 z2 granite 0 replace air

/fill x1 y1 z1 x2 y2 z2 air 0 replace stone

/fill x1 y1 z1 x2 y2 z2 stone 0 replace granite

Conjunction (logical "or") is done with a /clone using the masked option:

/clone x1 y1 z1 x2 y2 z2 dx dy dz masked normal

All of the other 2-argument boolean functions can be built up using combinations of

or

and

not

, making it possible to implement any combinatorial function in bitwise parallel form.


Restore starting configuration:

/fill 230 68 323 238 68 326 air 0

/fill 231 68 323 231 68 326 stone 0

/fill 235 68 324 238 68 324 sand 0

In range A:

change air to cobblestone:

/fill 235 68 323 238 68 326 cobblestone 0 replace air

change sand to air:

/fill 235 68 323 238 68 326 air 0 replace sand

Then clone A onto B with options masked normal

/clone 235 68 323 238 68 326 230 68 323 masked normal

In range B:

Negate the result:

/fill 231 68 323 234 68 326 granite 0 replace air

/fill 231 68 323 234 68 326 air 0 replace stone

/fill 231 68 323 234 68 326 air 0 replace cobblestone


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