CHP 2-Number System

8/13/2019 CHP 2-Number System

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LED 30303-

MICROPROCESSOR

BASED SYSTEM

CHAPTER 2:-

NUMBER SYSTEM

1


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2

Understand the concept of numbering and coding systems

Convert numbers in binary and hexadecimal into decimal equivalents

and vice versa

Represent binary and hex numbers using the complement systems

Addition of binary numbers Subtraction of binary numbers using complement systems

Perform multiplication and division of binary numbers

Logic Gates

OB

J

E

CT

I

V

E

S


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Human beings use base 10 (decimal)

arithmetic

There are 10 distinct symbols, 0, 1, 2, , 9

Computers use base 2 (binary) system

There are only 0 and 1

These two binary digits are commonly

referred to as bits

3

NUMBERING

AND

CODING

SYSTEMS(1)

Decimal andBinary Number

Systems


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Divide the decimal number by 2 repeatedly

Keep track of the remainders

Continue this process until the quotientbecomes zero

Write the remainders in reverse order to

obtain the binary number

4

NUMBERING

AND

CODING

SYSTEMS(2)

Converting fromDecimal to Binary

(1)


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5

Ex. 2:- Ex.3:-NUMBERING

AND

CODING

SYSTEMS(2)

Converting fromDecimal to Binary

(2)

RESULT

Note:it may not always be possible to

obtain an exact equivalent of the

fractional part of a number. The

accuracy depend on the number of

decimal places considered


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Know the weight of each bit in a binary

number

Add them together to get its decimalequivalent

Use the concept of weight to convert a

decimal number to a binary directly

Ex.

6

NUMBERING

AND

CODING

SYSTEMS(3)

Converting fromBinary to Decimal







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7

Base 16, the

hexadecimalsystem, is

used as a convenient

representation of binary

number

Ex.

It is much easier to

represent a string of 0sand 1s such as

100010010110 as its

hexadecimal equivalent

of 896H

NUMBERING

AND

CODING

SYSTEMS(4)

HexadecimalSystem


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To represent a binary number as its

equivalent hexadecimal number

Start from the right and group 4 bits at a time,

replacing each 4-bit binary number with its hex

equivalent

To convert from hex to binary

Each hex digit is replaced with its 4-bit binary

equivalent

8

NUMBERING

AND

CODING

SYSTEMS(5)

Convertingbetween Binary

and Hex (1)


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Ex 2:-

9

NUMBERING

AND

CODING

SYSTEMS(5)

Convertingbetween Binary

and Hex (2)


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Convert to binary first and then convert to

hex

Convert directly from decimal to hex byrepeated division, keeping track of the

remainders

10

NUMBERING

AND

CODING

SYSTEMS(6)

Converting fromDecimal to Hex

(1)


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11

Ex. 2:- Ex.3:-NUMBERING

AND

CODING

SYSTEMS(6)

Converting fromDecimal to Hex

(2)

Note:it may not always be possible toobtain an exact equivalent of the





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Convert from hex to binary and then to

decimal

Convert directly from hex to decimal bysumming the weight of all digits

Ex:-

12

NUMBERING

AND

CODING

SYSTEMS(7)

Converting fromHex to Decimal







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Adding the digits together from the least

significant digits

If the result is less than 16, write that digit as

the sum for that position

If it is greater than 16, subtract 16 from it to

get the digit and carry 1 to the next digit

13

NUMBERING

AND

CODING

SYSTEMS(8)

Addition of HexNumbers


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If the second digit is greater than the first,

borrow 16 from the preceding digit

14

NUMBERING

AND

CODING

SYSTEMS(9)

Subtraction ofHex Numbers


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The ASCII (pronounced ask-E) code

assigns binary patterns for

Numbers 0 to 9

All the letters of English alphabet, uppercase

and lowercase

Many control codes and punctuation marks

The ASCII system uses 7 bits to represent

each code

15

NUMBERING

AND

CODING

SYSTEMS(10)

ASCII Code


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Rules of Binary Addition

Ex.:- (without carry)

16

BINARY

ARITHMETIC

Binary Addition(1)


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Ex.:- (with carry)

17

BINARY

ARITHMETIC

Binary Addition(2)


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Rules of Binary subtraction

Ex.:-

18

BINARY

ARITHMETIC

Binary Subtraction


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BINARY

ARITHMETIC

Binary Subtractionusing Complement

(1)

Most microprocessor do not have a

subtraction circuitry

It is possible to do the subtraction by using

the complements Two types:-

1s complement

2s complement

1s complement or radix-minus-onecomplement is obtain by inverting each bit

of the binary number

e.g.:15510= %1001 1011 0110 0100

2s complement or radix-minus-twocomplement is obtain by inverting each bit

of the binary number and then adding 1 to

the least significant bit 19e.g.:15510= %1001 1011 0110 0100 => 0110 0101+ 1


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Ex.:-

Ex.:-

20

BINARY

ARITHMETIC


(2)


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BINARY

ARITHMETIC


(3)

Ex.:-

21


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Ex.:-

22

BINARY

ARITHMETIC


(4)


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23

BINARY

ARITHMETIC

Binary Number

256 possible combination of eight bits.


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Rules of Binary multiplication

Ex.:-

24

BINARY

ARITHMETIC

BinaryMultiplication

(1)

Note:The rules of binary multiplication

are the same as the truths of the AND

gate


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Another Method: Binary multiplication is

the same as repeated binary addition; add

the multicand to itself the multiplier

number of times.

Ex.:-

25

BINARY

ARITHMETIC

BinaryMultiplication

(2)


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Binary division is the repeated process of

subtraction, just as in decimal division.

Ex.:-

26

BINARY

ARITHMETIC

Binary Division(1)


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Ex.:-

27

BINARY

ARITHMETIC

Binary Division(2)


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Ex.:-

28

BINARY

ARITHMETIC

Binary Division(3)


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DIGITAL

PRIMER

Logic Gates

(1)


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30

DIGITAL

PRIMER

Logic Gates

(2)


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DIGITAL

PRIMER

Logic Gates

(3)


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CHP 2-Number System

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