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ch12/12.7/12.7.md

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# 12.7 Exercises for Section 12.7
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# Exercises for Section 12.7
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### 12.7.1
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### 12.7.2
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#### answer
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For each variable, we put it on one layer. Their is only two possible arrangement left 0 or left 1. So for each variable, we need at most two nodes for it. And we need only one node for the first variable. So the answer is:
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*2n-1*
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For example, when n is 4:
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![12.7.2](https://raw.github.com/fangang190/dragon-book-exercise-answers/master/ch12/12.7/assets/12.7.2.png)
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### 12.7.3
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#### answer
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There are two places to modify:
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a. BASIS: Zero variables. The BDD's must both be leaves, labeled either 0 or 1. The output is the leaf labeled 1 if `both` input are 1, or the leaf labeled 0 if `either` is 0.
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b. INDEUCTION 2. ...The first of these BDD's represents the function that is true for all truth assignments that have y<sub>1</sub> = 0 and that make `both` of the give BDD's true.
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b. INDEUCTION 2. ...The first of these BDD's represents the function that is true for all truth assignments that have y<sub>1</sub> = 0 and that make `both` of the give BDD's true.

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