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Ali.Z 21 Aug 2024, 11:11
https://en.wikipedia.org/wiki/Functional_completeness
they say a functional complete SET is a SET of AND,NOT. OR(A,B) = NOT(AND(NOT(A),NOT(B))) XOR(A,B) = AND(NOT(AND(A,B)),NOT(AND(NOT(A),NOT(B)))) ADD(A,B) = (A+B) ;sorry i cannot make addition using and not SUB(A,B) = NOT(ADD(NOT(A),B)) looking at the disassembly of these can be painful, imagine having more of these for other operations... like the xor the quite long, i can think of shl being even longer, i wouldnt use the word long tbh. things like ror, mul, div are extremely complex. _________________ Asm For Wise Humans 

21 Aug 2024, 11:11 

bitRAKE 21 Aug 2024, 11:37
ADD is the same as XOR, and the carry is AND.
_________________ ¯\(°_o)/¯ “languages are not safe  uses can be” Bjarne Stroustrup 

21 Aug 2024, 11:37 

macomics 21 Aug 2024, 13:53
ADD and SUB are mathematical operations, but the statement that AND and NOT are a complete set refers to logical operations. For functions with two arguments, there are only 16 of them. All 16 can be represented via the AND and NOT operations.
Code: X, Y = R {ZERO} 0, 0 = 0 0, 1 = 0 1, 0 = 0 1, 1 = 0 {AND} 0, 0 = 0 0, 1 = 0 1, 0 = 0 1, 1 = 1 {IMPY, AND(X, NOT(Y))} 0, 0 = 0 0, 1 = 0 1, 0 = 1 1, 1 = 0 {EQUX} 0, 0 = 0 0, 1 = 0 1, 0 = 1 1, 1 = 1 {IMPX, AND(NOT(X), Y)} 0, 0 = 0 0, 1 = 1 1, 0 = 0 1, 1 = 0 {EQUY} 0, 0 = 0 0, 1 = 1 1, 0 = 0 1, 1 = 1 {XOR} 0, 0 = 0 0, 1 = 1 1, 0 = 1 1, 1 = 0 {OR} 0, 0 = 0 0, 1 = 1 1, 0 = 1 1, 1 = 1 {NOR} 0, 0 = 1 0, 1 = 0 1, 0 = 0 1, 1 = 0 {EQU, NXOR} 0, 0 = 1 0, 1 = 0 1, 0 = 0 1, 1 = 1 {NOTY} 0, 0 = 1 0, 1 = 0 1, 0 = 1 1, 1 = 0 {NIMPX, NOT(AND(NOT(X), Y))} 0, 0 = 1 0, 1 = 0 1, 0 = 1 1, 1 = 1 {NOTX} 0, 0 = 1 0, 1 = 1 1, 0 = 0 1, 1 = 0 {NIMPY, NOT(AND(X, NOT(Y)))} 0, 0 = 1 0, 1 = 1 1, 0 = 0 1, 1 = 1 {NAND} 0, 0 = 1 0, 1 = 1 1, 0 = 1 1, 1 = 0 {ONE} 0, 0 = 1 0, 1 = 1 1, 0 = 1 1, 1 = 1 

21 Aug 2024, 13:53 

Ali.Z 23 Aug 2024, 06:06
bitRAKE wrote: ADD is the same as XOR, and the carry is AND. i dont get it, carry is AND? _________________ Asm For Wise Humans 

23 Aug 2024, 06:06 

revolution 23 Aug 2024, 06:11
If both input bits are 1 then the carry is 1. Therefore carry is the AND of the two bits.
Only works for the least significant bits. If you have more bits, then adding in the carry from the previous stage makes things a bit more complicated. 

23 Aug 2024, 06:11 

bitRAKE 23 Aug 2024, 08:06
Ali.Z wrote:
Code: half_adder: virtual at rsp+8 .A dd ?,? .B dd ?,? .param_bytes := $  $$ end virtual mov eax, [.A] mov edx, [.A] xor eax, [.B] ; sum and edx, [.B] ; carry retn .param_bytes full_adder: virtual at rsp+8 .A dd ?,? .B dd ?,? .C dd ?,? ; carry input .param_bytes := $  $$ end virtual ccall half_adder, [.A], [.B] mov ecx, edx ; partial carry ccall half_adder, eax, [.C] or edx, ecx ; carry retn .param_bytes _________________ ¯\(°_o)/¯ “languages are not safe  uses can be” Bjarne Stroustrup 

23 Aug 2024, 08:06 

Ali.Z 25 Aug 2024, 06:28
bitRAKE wrote: Here is another way to look at it ... thanks, it helped a lot to clear my mind. _________________ Asm For Wise Humans 

25 Aug 2024, 06:28 

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