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# Booleans
## Problem 1
`deg3.c` prints the a table listing the set of values of all 256 Boolean
functions of degree three to stdout.
## Problem 2
`sum-of-products.c` takes 2 natural numbers `n` and `f` from stdin, where `f`
is the encoded truth table of a Boolean function of degree `n`, for example,
| x0 | x1 | value |
| :---: | :---: | :---: |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
will be encoded as `0b0101 = 5`. The program then print the bitwise arithmetic
sum-of-products expression to stdout, e.g.
### Input
2 5
### Output
~x0&~x1 | ~x0&x1
## Problem 3
`k-map`, e.g.
### Input
0 0 0 1
0 0 1 0
0 1 0 1
1 0 0 0
1 1 1 0
0 1 1 0
1 1 0 1
1 0 1 0
### Output
00 01 10 11
0 1 0 1 1
0 0 0 0 0
## Problem 4
`threshold.c` takes in natural number `n`, a real threshold value `t` and `n`
weights, then `n` boolean values from stdin and print to stdout the output of
the given threshold gate, e.g.
### Input
7 0.25051534245890184
0.11609819805105248
0.7924365005827357
0.9835187780201641
0.4235209817923591
0.08303890030044114
0.7196176517110272
0.988645113198539
1 1 0 1 1 0 1
### Output
1
## Problem 5
`sum.c` takes similar input format from stdin and print the bitwise arithmetic
expression using only bit flip (`~`) and addition (`|`) to stdout, e.g.
### Input
3 69
### Output
~(~x0 | x1 | x2) | ~(~x0 | ~x1 | x2) | ~(~x0 | ~x1 | ~x2)
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