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by Dale Wick for AdamCon 13, July 13, 2001
It is often said that the world from a computer's perspective can be broken down into two camps. Those are variously called 0 and 1 or true and false or on and off. In electronics these are also 0 volts and +5 volts.
Now if you use the Adam, you probably have never spent time giving it instructions as a string of 0's and 1's. This is because the actual details are "abstracted" from you to make it easy to acomplish ever larger tasks.
abstraction is the process of hiding all of the details of the solution to a problem.
Today we will actually work with the following functions:
To work with these there is an abreviated notation:
A  B  !A  !B  AB  !(AB)  (!A) + (!B) 

0  0  1  1  0  1  1 
0  1  1  0  0  1  1 
1  0  0  1  0  1  1 
1  1  0  0  1  0  0 
Whenever you have a formula, you can translate it using the following substitutions.
A + 0 = A A + 1 = 1 A + A = A A + !A = 1 A + AB = A A!B + B = A + B AB + A!B = A AB + BC + (!A)C = AB + (!A)C 
A x 0 = 0 A x 1 = A A x A = A A x !A = 0 A(A + B) = A (A + !B)B = AB (A + B)(A + !B) = A (A + B)(A + C) = A + BC 
Change the formula in line 210 to each of the following:10 print "A","B","result" 100 a=0: b=0: GOSUB 200 110 a=0: b=1: GOSUB 200 120 a=1: b=0: GOSUB 200 130 a=1: b=1: GOSUB 200 199 END 200 REM The formula 210 c=a OR b 220 ? a,b,c 230 RETURN
Now we can prove some of the subsitutions using truth tables.210 c=NOT a 210 c=NOT (a AND b) 210 c=NOT (a OR b) 210 c=a AND b 210 c=a OR b 210 c=(a OR b) AND a<>b