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**Random Number Generator (RNG) for Microcontrollers**

Tom Dickens The Boeing Company

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**Introduction RNG Wisdom Motivation for an RNG Other RNG Methods**

Requirements for a “Good” RNG Approaches Taken Testing Implementation Summary Tom Dickens

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RNG Wisdom… “Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.” John von Neumann ( ). “The generation of random numbers is too important to be left to chance.” Robert R. Coveyou, Oak Ridge National Laboratory in Tennessee. Tom Dickens

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**Motivation For An RNG For Microcontrollers**

More Interesting Robotic Behavior Avoid Stuck-In-A-Corner Logic Used In AI Techniques Genetic Algorithms Neural Networks Fuzzy Logic Tom Dickens

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**Other RNG Methods Hardware-Based (true) RNGs**

White-Noise Source Transistor Circuits Our desire is to have a pseudo random number generator, as defined by… Tom Dickens

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**Requirements - a “Good” RNG**

Key Requirements (detailed list in paper). N = F(), where… N is in the range 0 to 255 Large cycle of N’s before pattern repeats. All values of N are generated the same number of times in the cycle. Windows of consecutive N’s in cycle meet… Constraints for Average, Min, and Max values. Small Code Size Tom Dickens

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**Approaches Taken Table-Based Method Define a table of 128 values.**

Use EXOR to generate 128 other values. Cycle through these 256 values 64 different ways. Cycle length of 16,384. Met the goodness criteria. 62 bytes of code bytes for table = 190 total bytes. 4 bytes of RAM. Tom Dickens

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**Approaches Taken Equation-Based Method 2-byte seed value in RAM**

seed = 181 * seed + 359 Return top 8 bits of seed. Cycle length of 65,536. Met the goodness criteria. 25 bytes of code, 4 bytes of RAM. Tom Dickens

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**Approaches Taken Notes:**

181 and 359 determined by a program searching for values to meet the goodness criteria. Table method also used a program to find right 128 table values. Tom Dickens

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**Generated Numbers First 240 numbers:**

Tom Dickens

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**Testing The Numbers Met The Defined Goodness Criteria Inspection**

Graphical Plots Plot number pairs on 256x256 grid. Tom Dickens

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Testing 1024 pairs plotted Tom Dickens

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Testing Half the pairs plotted Tom Dickens

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Testing All pairs plotted Tom Dickens

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Testing All pairs with another set of constants Tom Dickens

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**Implementation – 25 Bytes of 68HC11 Code**

Random: PSHB ; (1,3) Remember the current value of B * scratch = seed * multiplier LDAA #MULTIPLIER ; (2,2) A = #181 LDAB SEED_LOW ; (2,3) B = the low byte of the seed MUL ; (1,10) D = A x B STD RandomScratch ; (1,4) scratch = D LDAB SEED_HIGH ; (2,3) B = the high byte of the seed * low byte of MUL result is added to the high byte of scratch ADDB RandomScratch ; (2,3) B = B + scratch_high STAB RandomScratch ; (2,3) scratch = seed * 181 * LDD RandomScratch ; (2,4) D = scratch ADDD #ADDER ; (3,4) D = D + 359 STD RandomSeed ; (2,4) remember new seed value * (A = SEED_HIGH from ADDD instruction) PULB ; (1,4) Restore the value of B RTS ; (1,5) A holds the new 8-bit random number Tom Dickens

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**Summary RNG Studied RNG Goodness Criteria Developed**

Two RNG Methods Developed Both Methods Were Critiqued Equation-Based RNG Chosen For Number Coverage and Code Size 68HC11 Code Implemented and Tested Tom Dickens

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