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Art of Assembly Chapter 2

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I have a question about Randall Hyde''s book, AOA. It''s not a programming question, though, so I decided to post here. In Chapter 2: Boolean Algebra, Hyde talks about boolean functions: "If you fix the number of input variables, there are a finite number of unique boolean functions possible. For example, there are only 16 unique boolean functions with two inputs and there are only 256 boolean functions of 3 input variables. Given n there are 2**(2 to the nth power)(two raised to the two raised to the nth power) unique boolean functions of those n input variables. For two input variables, 2^(2*2)=2 to the 4th power or 16 different functions..." Now I don''t know a whole lot of math, at least not at this guy''s level. What does he mean by 2 raised to the 2... blah blah blah? If anyone knows what I''m talking about, can someone translate it for me? I can see from the context that there is a pattern-- 2 input variables would mean 16 possible functions; 3 inputs would mean 256; 4 would mean 65356. What is it exactly?

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I think it probably makes more sense if you continue reading to the next page, where he shows the actual 16 different states that you can judge two variables. Basically, it looks like what he really means is there are 16 ways you can compare two variables through boolean logic rules, such as AND, NOR, NOT, and even a COPY.

-nt20

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quote:
Original post by Some Guy

Now I don't know a whole lot of math, at least not at this guy's level. What does he mean by 2 raised to the 2... blah blah blah? If anyone knows what I'm talking about, can someone translate it for me?

I can see from the context that there is a pattern-- 2 input variables would mean 16 possible functions; 3 inputs would mean 256; 4 would mean 65356. What is it exactly?


This is a fairly straightforward combinatorics problem, which is why he didn't explain it more.

He's defining a function that maps number of inputs to the number of unique functions on those inputs.

This is expressed as 2^(2^n)
Where n is the number of inputs.

Edited by - cheesegrater on October 13, 2001 4:03:50 AM

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