# ch1. bottom of page 8, top of 9

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## ch1. bottom of page 8, top of 9

 I hope this is an acceptable place to ask this question. When reading the text on the pages listed in the title in the section titled 'Boolean Expressions' I am having trouble understanding how the boolean function used to specify the truth table is f(x,y,z) = (x + y) * /z. I understand that since y = 1, x + y would be 1. But since the value of z = 0 in the truth table, I don't understand how the 2nd part of the expression would be /0 (not 0)?
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## Re: ch1. bottom of page 8, top of 9

Here's the step-by-step solution for that row.
 Given x = 0 y = 1 z = 0 f = (x OR y) AND NOT z Solution f = (0 OR 1) AND (NOT 0) Substitute givens. f = 1 AND 1 Simplify. f = 1 Simplify.
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## Re: ch1. bottom of page 8, top of 9

 Thanks. I'm not understanding how given x = 0, y = 1, and z = 0 that that can be represented as f = (x OR y) AND NOT z.
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## Re: ch1. bottom of page 8, top of 9

 Administrator Ok. This paragraph is saying that a truth table is not the only way to specify a Boolean function; that a Boolean arithmetic expression can also represent the function. Line 3 by itself does not establish this fact. That's what the next sentence is trying to say; that all 8 of the lines must evaluate to a match to prove that the expression is an equivalent definition. This is basically the equivalent of saying that a multiplication table can also be represented the expression x*y. The table would more clearly show the equivalence if it had been two tables: ```Table 1a: Truth table definition of f(x, y, z) x y z || f(x, y, z) ------||----------- 0 0 0 || 0 ... || 1 0 1 || 1 ... ```Then present a table showing the equivalence of (x OR y) AND NOT z to f(x, y, z) ```Table 1b: Boolean expression definition of f(x, y, z) x y z || f(x, y, z) || (x+y)~z ------||------------||--------- 0 0 0 || 0 || 0 ... || || 1 0 1 || 1 || 1 ... ```
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## Re: ch1. bottom of page 8, top of 9

 Thanks, I'm not sure if I asked my question clearly. So I understand that for the example there are 3 inputs - X, Y, and Z and one possible output for each possible combination of inputs. I will try to draw a table to hopefully make my question clearer x     y     z     o(output) ---------------- 0     0     0     ? 0     0     1     ? 0     1     0     ? 0     1     1     ? 1     0     0     ? 1     0     1     ? 1     1     0     ? 1     1     1     ? I have two parts to the question and I'll ask the first then address then next part after. So, my first question is, how does one go about finding the output value for each row? I mean how does one know whether to AND x,y,z together, or OR x,y,z together or some combination of AND and OR? If the answer is, 'well that's where you plug in the values from the given boolean expression' - I can see that - but where did that boolean expression come from? Sorry this is all new to me and I'm feeling like I'm a little slow in picking this up :)