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LAB 1 Binary Numbers/ Introduction to C

Rajesh Rajamani

ME 4231

Department of Mechanical Engineering

University Of Minnesota

OVERVIEW

What is feedback control?

Binary and Hexadecimal Numbers

Working with the C Language

Tasks in Lab 1

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FEEDBACK CONTROL

Automatic control: Ensuring that one or more variables of interest are controlled to desired values

Examples Cruise control

Temperature control

Elevator control

The variables of interest are called “outputs”

“Control inputs” are utilized for achieving automatic control

“Disturbance inputs” might act on the system

The power of feedback – Explain

Sensors and actuators

BINARY TO DECIMAL CONVERSION

Binary

Decimal

01 221 x 0 x 01 201 220 x 1 x 10 1

012 2221 x 1 x 0 x 101 5

MSB LSB

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BINARY NUMBERS

Why are binary numbers needed in programming with data acquisition systems ?

The digital electronics in computers inherently store data as binary numbers

Counters, analog-to-digital-converters, and other systems on a data acquisition card measure electrical signals and convert them to binary numbers

Low cost embedded processors and microcontrollers do not have floating point units

It is computationally efficient to deal entirely with data in binary format

DECIMAL TO BINARY CONVERSION

104 Integer Remainder

104/2 52 0

52/2 26 0

26/2 13 0

13/2 6 1

6/2 3 0

3/2 1 1

1/2 0 1

Convert decimal number 104 to binary

Answer: 1101000104832642221 356 x 1 x 1 x

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HEXADECIMAL TO DECIMAL CONVERSION

Hexadecimal

Decimal

01 16161 x 0 x 01 16

01 1616 x 1 x 15 1 F 241

012 1616161 x 1 x 11 x 11 B 433

Hexadecimal numbers: Representation in terms of powers of 16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 1 2 3 4 5 6 7 8 9 A B C D E F

Decimal

Hexadecimal

DECIMAL TO HEXADECIMAL CONVERSION

104 Integer Remainder

104/16 6 8

6/16 0 6

Convert decimal number 104 to hexadecimal

Answer: 68

10489616166 01 x 8 x

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HEXADECIMAL TO BINARY

One hexadecimal digit gets replaced by 4 binary digits

Decimal: 104

Hexadecimal: 68

Binary: 0110 1000

6: 0110

8: 1000

ADDITION OF BINARY NUMBERS

0 + 0 = 0

1 + 0 = 1

1 + 1 = 10 i.e. 0 + carry 1

1 + 1 + 1 = 11 i.e. 1 + carry 1

Rules:

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ADDITION: EXAMPLE

Example

14 + 19 = 33

14: 0 1110

19: 1 0011

10 0001

33 32 2 x x 1121 05

SUBTRACTION OF BINARY NUMBERS

0 - 0 = 0

1 - 0 = 1

1 - 1 = 0

0 - 1 = 10 – 1 + borrow = 1 + borrow

Rules:

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SUBTRACTION: EXAMPLE

Example

27 - 14 = 13

27: 1 1011

14: 0 1110

0 1101

13 1 4 8 2 x 2 x x 023 1121

SIGNED NUMBERS

A positive number has 0 as the most significant bit

A negative number has 1 as the most significant bit

+ 15: 0 1111

- 15: ?? 1 1111 ????? NO

0 1111

1 1111

10 1110 0

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SIGNED NUMBERS

Need to use the 2’s complement to represent a negative number

2’s complement

First take 1’s complement

+15: 0 1111

1’s complement: 1 0000

Then add 1

+ 0 0001

1 0001

Hence -15: 1 0001

SIGNED NUMBERS

Check

+15: 0 1111

-15: 1 0001

10 0000

OK !

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INTERPRETING SIGNED NUMBERS

What is 1 0001 ?

Answer:

From the MSB, it is clear that it is a negative number

Therefore, first subtract 1

1 0001

0 0001

1 0000

Then take 1’s complement 0 1111

Hence the number is -15 !

SIGNED NUMBERS: EXAMPLE

Find – 18435 in hexadecimal

Step 1: First find +18435 in hexadecimal

18435 Integer Remainder

18435/16 1152 3

1152/16 72 0

72/16 4 8

4/16 0 4

Hence the hexadecimal equivalent of + 18435 is

4803

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SIGNED NUMBERS: EXAMPLE

Step 2: Convert to binary

4803 in binary is 0100 1000 0000 0011

Step 3: Take 1’s complement

1011 0111 1111 1100

SIGNED NUMBERS: EXAMPLE

Step 4: Add 1

1011 0111 1111 1100

1

1011 0111 1111 1101

Step 5: Convert back to hexadecimal

B 7 F D

Final answer: B7FD

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INTRODUCTION TO C

#include <stdio.h> void main() { float x, y; printf("\nEnter number"); scanf("%f",&x); printf("\n%f\n",x); y = x*x; printf("\nHere is the square of the number:%f\n\n",y); printf("Enter the number whose square you wish to find (q to quit)\n"); while(scanf("%f",&x) == 1) { printf("\nx=%f",x); y = x*x; printf("\ny=%f",y); printf("\nEnter the number whose square you wish to find (q to quit)\n"); } }

Example Program

FOR LOOPS

Syntax

for (k=0; k<5; k++)

{

printf(“%d\n”,k);

}

While loop syntax Covered last week

while( …..)

{

….

}

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ARRAYS

Example: Declaration of an array

The line

int count[10];

declares “count” to be an integer array of size 10.

In C, all arrays start with slot 0 (rather than slot 1)

Hence,

the first element in the array “count” is called count[0]

The last element in the array “count” is called count[9]

ARRAYS

An array can be declared with no initial values – Then its initial values are unpredictable

If an initializer is given, then array length may be omitted from the square brackets in the declaration statement

Example:

int count[] = {3,18,4,7,6,5,9,21,22,23};

Note that the size of the array count is not explicitly declared.

However, because of the initializer, count will be an array of size 10

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ARRAYS

The elements of an array can be accessed in 2 ways

Using subscripts

Using pointers

We will use subscripts in this lab.

Pointers will be covered in the next lab.

Example: Write a program to reverse order the elements of an array

Note: Task 2 in lab is to arrange the elements of an array in ascending order

ORDER ARRAY ELEMENTS

Determine th element, =0,1,2, ….,n

Find smallest number among elements , +1, +2,….,n

Place the smallest number in the th element

This can be done using 2 “for loops”

=0,1,2,3,…..,n

=i+1,i+2,i+3,…..,n

=0 =1

=i+1,i+2,….,n

Compare th element with th element and swap if th element is smaller

i i

i i

i

i

j

i

i i i

i

j

j

j

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TASKS IN LAB

Tasks are described in detail in handout Task 1

“Hello World” example

Task 2 Check addition of hexadecimal numbers from pre-lab

Task 3 Write a program to take in user input temperature and

convert temperature in Fahrenheit to Celsius

Task 4 Sorting elements in an array

Task 5 Introduction to Matlab, plotting

Important: Pre-labs, Post-labs