Ee2 chapter1 number_system

Apr 10, 2023

Lecturer Name [email protected]

Contact Number

IT2001PAEngineering Essentials (2/2)

Chapter 1 – Number System

2


IT2001PA Engineering Essentials (2/2)

Lesson Objectives

Upon completion of this topic, you should be able to: Convert numbers e.g. binary, octal, decimal,

hexadecimal and BCD from one system to another.



Specific Objectives

Students should be able to : Explain why the binary number system is ideal for digital

logic applications. Convert decimal whole numbers and fractional numbers

into binary numbers and vice versa. Convert decimal whole numbers into hexadecimal and

octal numbers and vice versa. Explain the term binary coded decimal. Convert BCD to decimal number and vice versa.

4



Application

In digital electronics,

only deal with two voltage levels; i.e.:

ON high or 1.

OFF low or 0.

Therefore almost all digital systems use

binary number system; i.e.: Base 2.

5



Number Systems

4 commonly used number systems:MSB LSB

• Decimal (Base 10) 2 5MSB LSB

• Binary (Base 2) 1 1 0 0 1MSB LSB

• Octal (Base 8) 3 1MSB LSB

• Hexadecimal (Base 16) 1 9

6



Binary Number SystemBinary number are strings of two (hence ‘bi’), symbols 0’s and 1’s, that represent numbers. They may be expanded in the usual way with a base of 2.

E.g. 11012

20

21

22

23

1048 +

1310

7



Binary System

Each digit in the binary number system is called a bit

A group of four bits binary number is known as Nibble.

A group of eight bits binary number is known as Byte.

Two bytes number form a word.

8



Binary to Decimal Conversion

Convert 111012 to decimal number

Whole number

111012

= (1)*24 + (1)*23 + (1)*22 + (0)*21 + (1)*20

= 1*16 + 1*8 + 1*4 + 0*2 + 1*1= 16 + 8 + 4 + 0 +1 = 2910

9



Try the following

Convert 101102 to decimal number

101102

= (1)*24 + (0)*23 + (1)*22 + (1)*21 + (0)*20

= 1*16 + 0*8 + 1*4 + 1*2 + 0*1= 16 + 0 + 4 + 2 + 0 = 2210

Solution

10



Binary to Decimal Conversion

Convert 101.1012 to decimal number

Fraction number

101.1012

= (1)*22 + (0)*21 + (1)*20 + (1)*2-1 + (0)*2-2 + (1)*2-3

= 1*4 + 0*2 + 1*2 + 1*0.5 + 0*0.25 +1*0.125= 4 + 0 + 1 + 0.5 + 0 + 0.125 = 5.62510

11



Try the following

Convert 110.112 to decimal number

110.112

= (1)*22 + (1)*21 + (0)*20 + (1)*2-1 + (1)*2-2

= 4 + 2 + 0 + 0.5 + 0.25 = 6.7510

Solution

12



Decimal to Binary Conversion

Convert 2510 to binary number by repeated division

Whole number

2 510

= 1 1 0 01212

2623212

02

Remainder

1001

1

LSB

MSB

212

25

13



Try the following

Convert 3010 to binary number

15

2723212

02

Remainder

0111

1

2 30

Ans

= 111102

Solution

14



Decimal to Binary Conversion

Convert 0.37510 to binary number by repeated multiplication

Fraction number

0.37510

= 0.0112

0.375 x 2 = 0.75

Carry

0

1

0.375 x 2 = 0.75

0.75 x 2 = 0.5

10.5 x 2 = 0

15



Try the following

Convert 13.12510 to binary number

6

2321202

Remainder

1011

2 13

Ans

= 1101.0012

0.125 x 2 = 0.25

Carry

0

00.25 x 2 = 0.5

10.5 x 2 = 0

Whole number Fraction number

Solution

16



Decimal to Octal conversion

Convert 48610 to Octal.

8 | 486 Remainder

8 | 60 6 LSB

8 | 7 4

8 | 0 7 MSB

48610 = 7468

Convert 0.61132510 to Octal.

Carry

0.611325 x 8 = 3.88 3 MSB

0.8906 x 8 = 7.125 6

0.125 x 8 = 1.00 1 LSB

0.61132510 = 0.3618

17



Octal to Decimal conversion

Convert 3268 to Decimal

2 1 0

3 2 68 = (3 x 8 ) + (2 x 8 ) + (6 x 8 )

= 192 + 16 + 6

= 21410

3 2 68 = 21410

2 1 0

weight

18



Decimal to Hexadecimal Conversion

Convert 49810 to Hexadecimal.

16 | 498 Remainder

16 | 31 2 LSB

16 | 1 F

16 | 0 1 MSB

49810 = 1F216

Convert 0.781493710 to Hexadecimal.

Carry

0.7814937 x 16 = 12.5039 C MSB

0.5039 x 16 = 8.0624 8

0.0624 x 16 = 1.00 1 LSB

0.781493710 = 0.C8116

19



Hexadecimal to Decimal conversion

Convert 2A616 to Decimal

2 1 0

2 A 616 = (2 x 16 ) + (A x 16 ) + (6 x 16 )

= 512 + 160 + 6

= 67810

2 A 616 = 67810

2 1 0

weight

20



Binary-Coded-Decimal System (BCD)

Used to represent each of the 10 decimal digits as a 4-bit binary code. Decimal BCD

0 0 0 0 0

1 0 0 0 1

2 0 0 1 0

3 0 0 1 1

4 0 1 0 0

5 0 1 0 1

6 0 1 1 0

7 0 1 1 1

8 1 0 0 0

9 1 0 0 1

10 0 0 0 1 0 0 0 0

21



Convert decimal number to BCD

3 5 7 910

0011 0101 0111 1001 (BCD)

Convert BCD to decimal number

0110 1000 0111 0011 (BCD)

6 8 7 310

22



Next Lesson

Documents

Ee2 chapter1 number_system