information sheet/kertas penerangan

INSTITUT KEMAHIRAN MARA BESUTJALAN BATU TUMBUH, ALOR LINTANG,22000 BESUT,TERENGGANU DARUL IMAN.

INFORMATION SHEET( KERTAS PENERANGAN )

PROGRAM’S CODE & NAME/ KOD DAN NAMA PROGRAM

EE-021-2:2012 INDUSTRIAL ELECTRONICS

LEVEL/ TAHAP L2

COMPETENCY UNIT NO. AND TITLE/ NO. DAN TAJUK UNIT KOMPETENSI

C02 INSTRUMENT AND TEST EQUIPMENT SETUP & HANDLING

WORK ACTIVITIES NO. AND STATEMENT/ NO. DAN PENYATAAN AKTIVITI KERJA

1. IDENTIFY INSTRUMENT AND TEST EQUIPMENT SET UP & HANDLING

2. PREPARE FOR INSTRUMENT AND TEST EQUIPMENT SET UP & HANDLING

3. SET UP INSTRUMENT AND TEST EQUIPMENT

4. PERFORM RECORDING AND TAGGING OF INSTRUMENT & TEST EQUIPMENT

5. REPORT INSTRUMENT AND TEST EQUIPMENT SET UP & HANDLING

CODE NO. / NO. KOD EE-021-2:2012-C02/P(2/15) Page/ Muka Surat: 1Of / Drpd : 16

TITLE/ TAJUK: NUMBER SYSTEMS IN DIGITAL

PURPOSE/ TUJUAN:

This information sheet purposes to explain details on number systems involved in digital

systems. The explanations related on binary number system, addition and subtraction

operations of binary number system including fractions and non-fractions, 1’s and 2’s

compliments of binary number and arithmetic operations and conversion of base in

numbering systems.

INFORMATION/ PENERANGAN:

The binary number system and digital codes are fundamental to computers and to

digital electronics in each general. In this chapter, the binary number and its

relationship to other number system such as decimal, hexadecimal and octal is

presented.

1. COUNT IN BINARY NUMBER SYSTEM

The binary number is simply another way to represent quantities. The binary

number system is less complicated than the decimal system because it has only

two digits. The two binary digits (bits) are I and 0. In a number system, this is

expressed as a base of 2. As with the decimal number system, each bit (digit)

position of a binary number carries a particular weight that determines the

magnitude of that number.

2. BINARY AND DECIMAL NUMBER CONVERSION

i. Convert From The Decimal Form To Binary Form – Without Fractions.

To convert from decimal to binary, use repeated division-by-2. For example, the

conversion of the decimal number I210 to binary by repeated division by 2.

Converting decimal number 12 to binary begin by dividing 12 by 2. Then divide

each resulting quotient by 2 until there is a 0 whole number quotient. The

reminder generates each division form the binary number. The first reminder to

be produced is the LSB (least significant bit) in the binary number and the last

reminder to be produced is the MSB (most significant bit).

CODE NO. / NO. KOD EE-021-2:2012-C02/P(2/15) Page / Muka Surat : 2Of / Drpd : 16

ii. Convert From The Decimal Form To Binary Form Involving Fractions.

Decimal fraction can be converted to binary by repeated multiplication-by-2. For

example, the conversion of the decimal number O.312510 to binary by repeated

multiplication by 2. Converting the decimal fraction 0.312510 to binary, begin by

multiplying 0.3125 by 2 and then multiplying each resulting fractional part of the

product by 2 until the fractional product is zero or until the desired number of

decimal places is reached. The carried digits, or carries generated by the

multiplications produce the binary number. The first carry produced is the MSB and

the last carry is the LSB.


iii. Convert From The Binary Form To Decimal Form.

The decimal value of any binary number can be found by adding the weights of all

bits that are I and discarding the weight of all bits that are 0. For an example the

conversion of the binary number 11011012 to decimal number as below:

iv. Convert From The Binary Form To Decimal Form Including Fractions.

Example the conversion of the binary fraction number 0.10112 to decimal number is

as below:

3. ADD AND SUBTRACT BINARY NUMBERS INCLUDING FRACTIONS

i. Addition Operation.

The four basic rules for adding two binary digits (bits) are as follows.


Example: Compute the addition operation of the binary number 1012 and 102

Example: Add the binary number 10102 and 112

Example: Add the binary number 110102 and 11002

ii. Subtraction Operation.

The four basic rules for subtracting bits are as follows.

Example: Subtract the binary number 10102 from 100012


4. 1’s AND 2’s COMPLIMENTS OF BINARY NUMBER

The 1’s and 2’s compliment of binary numbers are important because they permit

the representation of negative (-ve) numbers.

i. 1’s Compliment.

The 1’s compliment of a binary is found by changing all 1’s to 0s and all 0s to 1s. In

other words, change each of bits in the number to its complement. The operation is

compute as examples shown below.

Example: Find the 1’s compliment of

10110010


00011010

ii. 2’s Compliment.

The 2’s complement of a binary number is formed by taking the 1’s complement of

the number and adding 1 to the least significant bit (LSB) position.


10111000


00010110


5. EXPRESS SIGNED NUMBERS IN BINARY FORM

The left - most bit in a signed binary number is the sign bit, which tells you whether

the number is positive or negative. A 0 sign bit indicates a positive number, and a 1

sign bit indicates a negative number.

i. Sign Magnitude Form.

When a signed binary number is represented in sign - magnitude, the left - most bits

is the sign bit and the remaining bits are the magnitude bits. The magnitude bits are

in true (un-complemented) binary for both positive and negative numbers.

For example, the decimal number +25 is expressed as an 8-bits signed number

using the sign-magnitude form as shown below.

The decimal number -25 is expressed as 1 0 0 1 1 0 0 1. Notice that the only

difference between +25 and -25 is the sign bit because the magnitude bits are in

true binary for both positive and negative numbers. In the sign-magnitude form, a

negative number has the same magnitude bits as the corresponding positive

number but the sign bit is a 1 rather than zero.

ii. 1’s Complement Form.

Positive numbers in l’s complement form are represented the same way as the

positive sign-magnitude numbers. Negative numbers, however, are the 1’s

complements of the corresponding positive numbers. For example, using eight bits,

the decimal number -25 is expressed as the 1’s complement of +25 (00011001) as

11100110. In the 1’s complement form, a negative number is the 1’s complement of

the corresponding positive number.


iii. 2’s Complement Form.

Positive numbers in 2’s complement form are represented the same way as in the

sign-magnitude and 1’s complement forms. Negative numbers are the 2’s

complements of the corresponding positive numbers.

Example: Express decimal number -25 as 2’s complement.

In the 2’s complement form, a negative number is the 2’s complement of the

corresponding positive number.

Example: Express the decimal number -39 as an 8 bit number in the sign-

magnitude, 1’s complement and 2’s complement forms.

+39 = 00100111

In the sign-magnitude form -39 = 10100111

In 1‘s complement form -39,

In 2 ‘s complement form -39,


6. ARITHMETIC OPERATIONS WITH SIGNED NUMBERS

In this topic you will learn how signed numbers are added, subtracted, multiplied

and divided. Because the 2’s complement form for representing signed numbers is

the most widely used in computers and microprocessor-based systems, the

coverage in this topic is limited to 2’s complement arithmetic.

i. Addition In 2’s Complement System.

Let’s take one case at a time using 8-bit signed numbers as examples.

CASE 1: Two positive numbers. Add +7 with +4.

CASE 2: Positive number and smaller negative number. Add +15 with -6.

CASE 3: Positive number and larger negative number. Add +16 with -24.

CASE 4: Two negative number. Add -5 with -9.


CASE 5: Equal and opposite number. Add -9 with +9.

ii. Subtraction In 2’s Complement System.

Negate the subtrahend - will change the subtrahend to its equivalent value of

opposite sign while adding the negation to the minuend - the result will represent the

difference in between the subtrahend and minuend. Discard any final carry bit.

Example: Perform each of the following subtractions of the signed numbers.


7. CONVERSION OF BASE IN NUMBERING SYSTEMS

i. Octal to Binary Conversion.

Because each octal digit can be represented by a 3-bit binary number, it is very

easy to convert from octal to binary. Each octal digit is represented by three bits as

shown below.

Example: Convert each of the following octal numbers to binary.

a) 138 b) 258 c) 1408 d) 72568

ii. Binary to Octal Conversion.

Example: Convert each of the following binary numbers to octal.


iii. Binary to Hexadecimal Conversion.

The hexadecimal number system has sixteen digits and is used primarily as a

compact way of displaying or writing binary numbers because it is very easy to

convert between binary and hexadecimal.

Hexadecimal is widely used in computer and microprocessor application. The

hexadecimal number system has of sixteen; that is it is composed of 16 digits and

alphabetic characters. Most digital systems process binary data in groups that are

multiples of four bits, making the hexadecimal number very convenient because

each hexadecimal digit represents a 4-bit binary number as listed below.

Example: Convert the following binary numbers to hexadecimal.

DECIMAL BINARY HEXADECIMAL0 0 0 0 0 01 0 0 0 1 12 0 0 1 0 23 0 0 1 1 34 0 1 0 0 45 0 1 0 1 56 0 1 1 0 67 0 1 1 1 78 1 0 0 0 89 1 0 0 1 910 1 0 1 0 A11 1 0 1 1 B12 1 1 0 0 C13 1 1 0 1 D14 1 1 1 0 E15 1 1 1 1 F


iv. Hexadecimal to Binary Conversion.

Example: Determine the binary numbers for the following hexadecimal numbers.


QUESTION/ SOALAN:

Answer all the questions.

1. Compute the following operation.

2. Determine the positional value of 7 of the following.

i. 17 = ________________________________________

ii. 70 = ________________________________________

iii. 117 = ________________________________________

iv. 276 = ________________________________________

v. 8794 = ________________________________________

3. Compute the following sign-magnitude operations.

i. (-11) + (-23).

ii. (+3) + (-7).


2 X 101 + 8 X 100 =

4. Convert each of the following base to decimal.

i. 10012 = _____________________

ii. A16 = _____________________

iii. 4F16 = _____________________

iv. 01012 = _____________________

v. 138 = _____________________


REFERENCE/RUJUKAN:

1. Ronald J. Tocci (Fifth Edition, 2008). Prentice Hall International., Digital System

– Principle and Application. Pages : 132 till 150.

2. Tocci., Widmer., Moss (Tenth Edition, 2013). Pearson International Edition.,

Digital System – Principle and Application. Pages : 115 till 135.

3. Floyd (Ninth Edition, 2010). Pearson Prentice Hall., Digital Fundamental. Pages :

145 till 163.

4. Nigel P. Cook (2010). Prentice Hall., Introductory Digital Electronic. Pages : 112

till 125.

5. William Kleitz (Fifth Edition, 2011)., Prentice Hall., Digital Electronics – A

practical Approach. Pages : 110 till 132.


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