Intro to Computer Engineering

Assignment 1 - Finite State Binary Counter

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Access your repository

Click here to access the Canvas page with the repository for this assignment.

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The idea

This assignment contains two parts: binary puzzles and a binary counter. In this assignment you will: a) use bitwise and Boolean operators to solve basic logical operations on numbers and b) use finite-state machines to model a binary counter. These logic puzzles will help you better understand how binary fits into the day-to-day mechanics of computing. In other words, this assignment will help you think about how computers actually look at and understand data that they interact with. image

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Objectives

By the end of this assignment, you should know:

Part I Binary Puzzles

Part II Binary Counter

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The background

Bitwise and Boolean operators

It’s hard to talk about numbers at all without talking about operators. You should be familiar with many of them already: +, -, *, etc. They take one or two numbers and operate on them, changing them. We introduce two new groups of operators: bitwise operators and Booleans ones.

Bitwise operators are operators that act directly on the individual bits of a binary number, whereas Boolean operators (also known as logical operators) operate on the “logical values” that the complete number represents: in Arduino, 0 is a logical false, and anything else is true (even -1).

In a sense, these two groups of operators are very closely related: both operate only on two values (Boolean operators treat everything as either true or false, and bitwise operators operate on the underlying bits of numbers which can each only be 0 or 1), and as you’ll see in a bit, they perform very similar operations on these values. Their main difference is their scope: bitwise operations work on each bit individually, whereas Boolean operations work on the numbers as a whole.

The operations proper

Characters, integers, & longs

Not all numbers are the same length. Because of this it is useful to have several different data types that we can choose from for storing differently sized numbers. In this way we don’t waste space storing small numbers in large spaces. The three data types we will use in this lab are characters (char: 1 byte), integers (int: 2 bytes), and longs (long: 4 bytes), each of which store whole numbers.

By default, all of these values are signed and can store both positive and negative numbers. Their possible values range from and , where n is the number of bits in the data type. unsigned numbers range from 0 to . e.g. unsigned char, unsigned int and unsigned long.

Two’s complement is used here to store signed numbers. If you still have confusions about signed and unsigned numbers, please read Introduction to Information Representation guide for detailed explanations.

Note: Data types in Java or C have different lengths than in Arduino C.

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The Assignment

Part I Binary Puzzles


Open the Arduino sketch called binaryPuzzles.

  1. Bit shifting!

    Complete the functions shiftRight and shiftLeft.

    • unsigned shiftRight(unsigned num, int n): Shift num to the right n bits.
    • int shiftLeft(int num, int n): Shift num to the left n bits.
  2. Bit manipulations!

    For each function below, use only the bitwise and Boolean operators listed above (i.e., no if-then tests, comparisons (e.g., ==, !=, >, <, >=, <=), arithmetic operators (e.g., *, +, -, /, %) or for/while loops are allowed) to write functions that return 1 if the input matches the condition given and 0 otherwise. You may use constant values (e.g., 0, 1, 255, etc.) in your operations. You should be able to solve each in one line.

    • int hasAOne(int num): At least one bit in num is a one (Binary Representation).
      E.g. 7 is 111 in base 2. Therefore hasAOne(7) should return 1(true).
    • int hasAZero(int num): At least one bit in num is a zero.
    • int leastSigByteHasAOne(int num): At least one bit in the least significant byte(the last byte) of num is a one. (This is NOT just testing whether the lest significant bit is a one.
    • int isNegativeInt(int num): the integer num is negative.
      Hint: We use Two’s complement to represent signed numbers.
    • int isNegativeLong(long num): the long num is negative. Remember, in Arduino C longs are 4 bytes (32 bits) in length.
    • int isNegativeChar(char num): the char num is negative. Remember, in Arduino C chars are 1 byte (8 bits) in length.
    • int negate(int num): Return the two’s complement negation of num. This function should return a number instead of 1 or 0 (true or false).
      Exception: You are allowed to use the + operator for this one (not allowed for the functions above).

Part II Binary Counter

This part has two components: drawing a FSM, and modeling said FSM on your Arduino.

Setup

The Model

The Studio has useful information for this lab. If you were unable to finish the studio last class we recommend you look it over before starting on the assignment.

Interpreting FSMs and FSAs

Here is the drawing of the Studio 1 FSM:

Simple Binary Counter

For more information on how to create effective FSMs, watch a short video here.

Drawing Your Model

The Program

Transferring FSMs to Code

Here is an Example of an Enum in Arduino C:

enum Direction {
  	 North,			// North = 0
  	 East,			// East = 1
  	 South,			// South = 2
  	 West			// West = 3
} direction = North;

Here is some pseudocode to demonstrate switch:

month = 2
switch (month) {
	case 1:
		print 'January'
		break
	case 2:  		// switch to case 2 because month == 2
		print 'February' 	
		break		// break so other cases won't run
	case 3:
		print 'March'
		break
	... 
}
Adding the Reverse Button
The Final product

Your Output should look close to this:

Final Product

We also accept reversing after the next state change, as shown in this older video. Note that it also showed state bits in the incorrect order (least significant bit leftmost rather than rightmost).

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The check-in

  1. Commit and push your code (and FSM), then verify in GitHub that it is all there.
  2. Follow the checklist below to see if you have everything done before demoing your assignment to a TA.
    • Part I Binary Puzzles
      • All functions work correctly and only contain the approved operators (45 points)
        • shiftRight(int num, int n)
        • shiftLeft(int num, int n)
        • hasAOne(int num)
        • hasAZero(int num)
        • leastSigHasAOne(int num)
        • isNegativeInt(int num)
        • isNegativeLong(long num)
        • isNegativeChar(char num)
        • negate(int num)
    • Part II Binary Counter
      • Drawn FSM (20 points)
        • 16 states
        • correctly models the counter
      • FSM (30 points)
        • determineNextState() filled out and working
        • 16 states
        • uses enums
        • switches from state to state with switch or if statements
        • working counter printed out in the Serial Monitor
      • Reverse Button / Lever (5 points)
        • can switch the direction of the counter
    • All of your files are committed
  3. Assignment Demo
0  :  000
1  :  001
2  :  010
3  :  011
4  :  100
--Reverse--
3  :  011
2  :  010
1  :  001
--Reverse--
2  :  010
3  :  011
--Reverse--
2  :  010
1  :  001
0  :  000
7  :  111
6  :  110
5  :  101
--Reverse--
6  :  110
7  :  111
0  :  000
--Reverse--
7  :  111
6  :  110
5  :  101
4  :  100
  1. Check out with a TA.

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Page written by Sean Schaffer, Claire Heuckeroth, Ben Stolovitz and Shuya Ma.