COURSE WORK MTE 3101

NAME : HARYATI BINTI ISMAIL.

I/C NO : 900109-03-5164.

LECTURER : DR ROSMAWATI BT MUSA.

QUESTION

1. An International Standard Book Number (ISBN) is used to identify books. The

ISBN numbers for a certain book is 0-534-36890-5. The last digit is called the

check digit and is used as follows. Multiply the first digit by 10, the next digit by 9,

and so on :

10(0) + 9(5) + 8(3) + 7(4) + 6(3) + 5(6) + 4(8) + 3(9) + 2(0) + 1(5) = 209

This number is congruent to 0, (mod 11). This is not by chance. The check digit,

5, is chosen so that this sum is 0, (mod 11). In other words, the check digit x for

the book with ISBN number 0-534-34015-x is found by considering

10(0) + 9(5) + 8(3) + 7(4) + 6(3) + 5(4) + 4(0) + 3(1) + 2(5) = 148 ≡ 5

This means that for check digit x, 5+x ≡ 0,(mod 11).The one-digit solution to this

equation is x=6, so the check digit is 6.

What is the check digit for the book with the given ISBN in Problems (a) – (d).

(a) 0-534-13728-x

(b) 0-434-16778-x

(c) 0-784-13768-x

(d) 0-924-18828-x

SOLUTION

1.

(a) 0-534-13728-x

10(0) + 9(5) + 8(3) + 7(4) + 6(1) + 5(3) + 4(7) + 3(2) + 2(8) = 168 ≡ 3

= 3(mod 11)

3+x=0 (mod 11)

3+x=11

x=8

To check the answer,

Substitute the value of x

10(0) + 9(5) + 8(3) + 7(4) + 6(1) + 5(3) + 4(7) + 3(2) + 2(8) + 1(8) = 176 ≡ 0

Hence, the check digit is 8.

(b) 0-434-16778-x

10(0) + 9(4) + 8(3) + 7(4) + 6(1) + 5(6) + 4(7) + 3(7) + 2(8) = 189 ≡ 2

= 2(mod 11)

2+x=0 (mod 11)

2+x=11

x=9

To check the answer,

Substitute the value of x.

10(0) + 9(4) + 8(3) + 7(4) + 6(1) + 5(6) + 4(7) + 3(7) + 2(8) + 1(9) = 198 ≡ 0

Hence, the check digit is 9.

This means that for check digit x, 3+x ≡ 0,(mod 11).

The one-digit solution to this equation is x=8, so the

check digit is 8.

This means that for check digit x, 2+x ≡ 0,(mod 11).

The one-digit solution to this equation is x=9, so the

check digit is 9.

(c) 0-784-13768-x

10(0) + 9(7) + 8(8) + 7(4) + 6(1) + 5(3) + 4(7) + 3(6) + 2(8) = 238 ≡ 7

= 7(mod 11)

7+x=0 (mod 11)

7+x=11

x=4

To check the answer,

Substitute the value of x

10(0) + 9(7) + 8(8) + 7(4) + 6(1) + 5(3) + 4(7) + 3(6) + 2(8) + 1(4) = 242 ≡ 0

Hence, the check digit is 4.

(d) 0-924-18828-x

10(0) + 9(9) + 8(2) + 7(4) + 6(1) + 5(8) + 4(8) + 3(2) + 2(8) = 225 ≡ 5

= 5(mod 11)

5+x=0 (mod 11)

5+x=11

x=6

To check the answer,

Substitute the value of x

10(0) + 9(9) + 8(2) + 7(4) + 6(1) + 5(8) + 4(8) + 3(2) + 2(8) + 1(6) = 231 ≡ 0

Hence, the check digit is 6.

This means that for check digit x, 7+x ≡ 0,(mod 11).

The one-digit solution to this equation is x=4, so the

check digit is 4.

This means that for check digit x, 5+x ≡ 0,(mod 11).

The one-digit solution to this equation is x=6, so the

check digit is 6.