From a3dd2581ed4847670f81157091016c14ca18803d Mon Sep 17 00:00:00 2001
From: Nguyễn Gia Phong <vn.mcsinyx@gmail.com>
Date: Tue, 14 Jan 2020 18:29:11 +0700
Subject: [usth/MATH2.3] Mathemate Discretely

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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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