http://www.allaboutcircuits.com/vol_4/chpt_7/4.html
I think I have brought this up before, but am not sure.
The E-book includes the distributive property of AND over OR, namely
A(B+C) = AB + AC
But fails to mention the distributive property of OR over AND, namely
A+BC = (A+B)(A+C)
This is a very useful property that most people don't know about because it goes against the fact that we have long sense internalized the notion that addition does not distribute over multiplication the way that multiplication distributes over addition.
As an aside, I don't think it is a good idea to call the OR operation "addition" and the AND operation "multiplication" for just this reason. We are not adding or multiplying anything -- we are ANDing and ORing. We are merely using the same symbols for these operations as we do for addition and multiplication. I think that misusing the names of the arithmetic operations in place of the Boolean algebraic ones leads to the misperception that the rules of arithmetic algebra and those of Boolean algebra are the same when, clearly, they aren't. This is one of the reasons why more math-oriented treatments use different symbols (¬, ∧, ∨) and operation names (negation, conjunction, disjunction) entirely
But that's a pedagogical point that I'm sure has proponents on both sides aplenty.
I think I have brought this up before, but am not sure.
The E-book includes the distributive property of AND over OR, namely
A(B+C) = AB + AC
But fails to mention the distributive property of OR over AND, namely
A+BC = (A+B)(A+C)
This is a very useful property that most people don't know about because it goes against the fact that we have long sense internalized the notion that addition does not distribute over multiplication the way that multiplication distributes over addition.
As an aside, I don't think it is a good idea to call the OR operation "addition" and the AND operation "multiplication" for just this reason. We are not adding or multiplying anything -- we are ANDing and ORing. We are merely using the same symbols for these operations as we do for addition and multiplication. I think that misusing the names of the arithmetic operations in place of the Boolean algebraic ones leads to the misperception that the rules of arithmetic algebra and those of Boolean algebra are the same when, clearly, they aren't. This is one of the reasons why more math-oriented treatments use different symbols (¬, ∧, ∨) and operation names (negation, conjunction, disjunction) entirely
But that's a pedagogical point that I'm sure has proponents on both sides aplenty.