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A programmable prototype to achieve Turing machines | |
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| Calculateurs |
| A) CALCULATIONS WITH NUMBERS WRITTEN IN UNARY | |||||
| Addition of 2 unaries Solution 1 2 states |
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| Addition of 2 unaries Solution 2 Copy X to the right of Y 5 states |
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| Subtract X from Y with X < Y 3 states |
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| Multiplication of two integers written in unary 10 states |
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| Euclidean division by 3 in unary 8 states |
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| Calculation of N modulo p in unary N > 0 and p > 0 7 states |
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| Euclidean division of A by B in unary 9 states |
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| Calculation of 2 n in unary
The machine treats the unary as the binary to which it will add 1 to obtain 2 n 6 states |
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| Comparison of two unaries 8 states |
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| B) Unary to binary and binary to unary passages | |||||
| Writing a unary in binary 5 states |
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| Writing a binary to unary 6 states |
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| C) CALCULATIONS WITH BINARY NUMBERS | |||||
| Add 1 to a binary number 1 state |
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| Subtract 1 from a binary 1 state The binary is > 1 |
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| Addition of 2 binary numbers 6 states |
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| Subtract one binary from another 6 states We assume X > Y > 0 |
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| Difference of 2 binary with deletion of 0 9 states We assume X > Y > 0 |
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| Product of 2 binary numbers X and Y X is written every other box least significant bit on the right Y : least significant bit on the left 11 states |
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| Calculation of 3n in binary Multiply a binary by 11 3 States |
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| Calculation of 3n + 1 in binary 4 states |
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| Calculation of 3n + 2 in binary 4 states |
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| Division by 11 with divisibility test and suppression of mute 0s. 11 states |
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| Calculation of 5n in binary Multiply a binary by 101 5 States |
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| Calculation of 5n + 1 in binary 6 states |
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| Calculation of 5n + 2 in binary 6 states |
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| Calculation of 5n + 3 in binary 6 states |
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| Calculation of 5n + 4 in binary 6 states |
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| Dividing a binary by 101 10 states |
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| Passage of the binary system to the Gros-Gray code 2 states |
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| Passage of the Gros-Gray code to the binary system 2 states |
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