Chapter 1

•Identification Numbers

•Check Digits

•Codes

Identification Numbers

Area Number-Group Number-Serial Numberpg 3-5

Where was the mailing address of your SSN?

ISBN - Find the one for our book

VIN

UPC Codes

First digit - type of item - pg 9 Manufacturer code Product code

Check Digits

An additional digit added to an identification number so that a transmission error may be found.

Check Digits

An additional digit added to an identification number so that a transmission error may be found.

Before we look at how check digits are used we need to look at some special rules.

Did you know that each of these numbers is divisible by 9?

81135

23616

Did you know that each of these numbers is divisible by 9?

8113523616

Do you know why?

If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.81: 8+1=

135: 1+3+5=

23616: 2+3+6+1+6=

Name a number that is divisible by 9.

Ex. 1.3A biology professor has nearly 1000

students in his class. For reasons of confidentiality he wants to assign each student an identification number.

Suggest some ways to assign these identification numbers.

The professor could assign a fourth digit as a check digit. One way to do this is to assign the fourth digit so that the the identification number is divisible by 9.

A 3 digit number that does not contain a 9 could be assigned and then the 4th digit makes the sum of the 4 digits divisible by 9.

If the sum of the 3 digits is already divisible by 9 the 4th digit will be a 0.

This is one example of a check digit.

We will look at more check digits in the next section.

1.1 AssignmentPg 12

(3,9,11,13,15,19,25,26,33)

Section 1.2Modular Arithmetic and Check-

Digit Schemes

Modular Arithmetic and Check-Digit Schemes

How do we know if this is a legitimate VIN number?

Before looking at how to check a VIN for legitimacy, lets look at a simpler example.

Divide 4 by 13

Before looking at how to check a VIN for legitimacy, lets look at a simpler example.

Divide 13 by 4

The quotient is:

3 with remainder 1

Before looking at how to check a VIN for legitimacy, lets look at a simpler example.

Divide 13 by 4

The quotient is 3 with remainder 1

To check: 4 X 3 + 1 = 13

If a number divides evenly and the remainder is zero:

For example: 15/5 = 3

We can say “5 divides 15”

This can be written 5|15

The remainder is the important number.

Division by 7Integer Remainder

. . . , -21, -14, -7, 0, 7, 14, 21, . . . 0

. . . , -20, -13, -6, 1, 8, 15, 22, . . . 1

. . . , -19, -12, -5, 2, 9, 16, 23, . . . 2

. . . , -18, -11, -4, 3, 10, 17, 24, . . . 3

. . . , -17, -10, -3, 4, 11, 18, 25, . . . 4

. . . , -16, -9, -2, 5, 12, 19, 26, . . . 5

. . . , -15, -8, -1, 6, 13, 20, 27, . . . 6

What patterns do you see?

In every row, the difference between the numbers in a row is a multiple of 7

Integer Remainder. . . , -21, -14, -7, 0, 7, 14, 21, . . . 0. . . , -20, -13, -6, 1, 8, 15, 22, . . . 1. . . , -19, -12, -5, 2, 9, 16, 23, . . . 2. . . , -18, -11, -4, 3, 10, 17, 24, . . . 3. . . , -17, -10, -3, 4, 11, 18, 25, . . . 4. . . , -16, -9, -2, 5, 12, 19, 26, . . . 5. . . , -15, -8, -1, 6, 13, 20, 27, . . . 6

The language we will use is:

The two numbers are: “congruent modulo 7”

Because 7 divides the difference between 29 and 15:

7|(29-15) and 29=15 mod 7

(= should be a symbol with 3 lines)

IntegerRemainder

. . . , -21, -14, -7, 0, 7, 14, 21, . . . 0

. . . , -20, -13, -6, 1, 8, 15, 22, . . . 1

. . . , -19, -12, -5, 2, 9, 16, 23, . . . 2

. . . , -18, -11, -4, 3, 10, 17, 24, . . . 3

. . . , -17, -10, -3, 4, 11, 18, 25, . . . 4

. . . , -16, -9, -2, 5, 12, 19, 26, . . . 5

. . . , -15, -8, -1, 6, 13, 20, 27, . . . 6

State 2 more congruence relationships.

See the Example 1.11 on pg 24

See example 1.12 on pg 24

Modular Check Digit Schemes

9 is a popular check digit

Ex. A company uses a mod 9 check-digit scheme for its 5 digit id number. The 5th digit is the check digit.

Determine the check digit for

5368

Determine the check digit for

5368

Add the digits:5 + 3 + 6 + 8 = 22

9|(22 - ?)

9|18, so

9|(22 - 4)

The check digit is 4

Find the missing digit if the 5th digit is the check-digit using mod 9:

73?11

7 + 3 + d3 + 1 = 1 mod 9

Remember, the 5th digit is the check digit

7 + 3 + d3 + 1 = 1 mod 9

11 + d3 = 1 mod 9

What number minus 1 is divisible by 9?

19=1mod 9 or 9|(19-1)

11 + d3 = 1 mod 9

What number minus 1 is divisible by 9?

19=1mod 9 or 9|(19-1)

What does d3 have to equal?

11 + d3 = 1 mod 9

What number minus 1 is divisible by 9?

19=1mod 9 or 9|(19-1)

What does d3 have to equal?

d3 = 8

Example of uses of mod 9 check-digits:

Money Orders

European Currency

Airline tickets use a mod 7 check digit system. Read ex 1.7 on pg 29.

Assignment for sec. 1.2:Pg 32 (9,21,23,25,31,33,35)

Binary CodesMorse CodeUPCBrailleASCII

Section 1.3Encoding Data

A data coding system made up of two states (on/off) or two symbols

Binary Codes

Morse code is one type of a binary code.

See chart on pg 38

Morse Code

A dot is one unit ONA dash is 3 units ONThe circuit is OFF for 1 unit between dots and dashes

Morse Code

Morse Code

The dots and dashes can be converted to black and white squares

Black square = ONWhite square = OFF

Morse Code

The black and white squares can be converted to 1’s and 0’s

1 = ON0 = OFF

See chart on pg 39

Morse Code

Convert the word MATH to Morse Code using 1’s and 0’s

Insert 3 0’s between letters.

Morse Code

Convert a list of 1’s and 0’s into English.

See ex. 1.19 on pg 39

Morse Code

UPC Bar Codes

The first 5 digits are the manufacturer code

The 2nd 5 digits are the product code

UPC Bar Codes

The last digit is a check digit chosen according to the following rule:

3(d1+d3+d5+d7+d9+d11) +1(d2+d4+d6+d8+d10+d12) =

0mod10*The total is divisible by 10

UPC Bar Codes

Braille

Each letter consists of 6 dots.

Each dot is either raised or not raised.

For a combination of 2x2x2x2x2x2 characters

Braille

2x2x2x2x2x2 = 26 = 64

Possible characters

Braille

More than 64 characters were needed for computers so the ASCII code was developed.

ACSII

A bit is a information unit having one of two states:

On or Off1 or 0

ACSII

A groups of 8 bits is called a byte.

This would be a set of 8 1’s and 0’s.

ACSII

ASCII code is an 8-bit code.

See Table 1.14 on pg 48.

ACSII

How many characters could an 8-bit code represent?

ACSII

How many characters could an 8-bit code represent?

28 = 256

ACSII

Pg 51 (1,7,9,11,13,15,17,21,25a,b,29)

Section 1.3 Assignment

Send me an e-mail so that I have your address.

lesa@nossi.com

Pg 12 (3,9,11,13,15,19,25,26,33)Pg 32 (9,21,23,25,31,33,35)Pg 51 (1,7,9,11,13,15,17,21,25a,b,29)

Chapter 1 Assignment