3 digital representation

8/8/2019 3 Digital Representation

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HELLO THERE


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Introduction Why digital

Advantages: Easy todesign

Information storage is easy

Accuracy and precision are greater

Operation can be programmed

Less effected by noise

Smallin size

Disadvantage: Needs conversion process analog digital - analog


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Introduction DigitalICs collection of resistors, diodes andtransistors

fabricatedon a single piece of semiconductor materialcalledchip

Package type DIP / PDIP Dual-In-Line Package / PlasticDual-In-Line Package SOIC Small Outline Integrated Circuit TQFP Thin-Quad Flatpack Package QFN - Quad FlatNo Lead Package PLCC Plastic Leaded Chip Carrier


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IntroductionCategorizations of chips:

6 levels of circuit complexity

1. SmallScale Integration (SSI) >12gates

2. Medium Scale Integration (MSI) 12 99 gates

3. Large Scale Integration (LSI) 100 9999 gates

4. Very LSI (VLSI) 10,000 99,999 gates

5. Ultra LSI (ULSI) 100,000 999,999 gates

6. Giga LSI (GSI) >1 million gates


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Introduction Mostcommon numbering system:

Decimal -> 1234567

Binary -> %01101010

Octal -> @234567

Hexadecimal-> $12CD


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Introduction Codes:

signedandunsigned number ,

BCD,

Gray Code,

American Standard Code for Information

Interchange (ASCII)code, Alphanumericcode,


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SignedNumber Mostcommon signed numbers are

Sign-magnitude number

1s complementnumber

2s complementnumber

Normally, 0is a sign for + and1is -.


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Sign Magnitude Mostsimplest butimpracticalto be

implementedin computer system.

Format:

MSB sign ofthe number

Other magnitude


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1s Complement Change each bitby its complement.

0 -> 1

1 -> 0


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2s Complement 1s complement+ 1to LSB.

Tips: The 2s complementcan be obtained for a

binary number by duplicating each bit fromLSBuntilit reaches the B1.

The restmustbe complemented.


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Binary-Coded-Decimal (BCD) 4 bit represent each digit

Types BCD8421 (commonly Known as BCD)

BCD6221

BCD4221


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Binary-Coded-Decimal (BCD) Question:-

Change the followingdecimal numberintoBCD

21

99

54

23


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Change the followingdecimal numberintoBCD6221

21

99

54

23


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Change the followingdecimal numberintoBCD4221

21

99

54

23


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Excess-3 Usedon older computers.

Biased by 3


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Excess-3 Question:-

Change the followingdecimal numberinto Excess-3

12

21

11

2343


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ASCII


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ASCII Question:-

Change the followingdecimal numberintoASCII

12

21

11

23 43


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Binary Floating Point Away to represent floating point

Can be either

32 bitsingle precision (S - 31, E - 23-30, F 0-22)

64 bitdouble precision

(S 63, E 51-62, F 0-51)


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Binary Floating PointExample:


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Binary Floating Point3. Thatnumber is then normalized;the binary pointis

movedleft, leavingonly a1toits left.4. The number of places itis movedgives the (power

oftwo) exponent1110110.101 becomes1.110110101 x 26.

5. After this process, the firstbinary digitis always a1, soitis need notbe includedin the encoding. Therestis the parttothe rightofthe binary point,

which is then paddedwith zeros on the righttomake 23 bitin all.6. The exponentis 6 and should be biased by +127.

Thus, exponentialis 6+127=133 (10000101)


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Binary Floating Point


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Binary Floating Point Question:

Convertthe followingdecimal numbertoa 32 bitsingle precision binaryfloating point.

-12.5

234.25

21.625


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Gray Code Code where only one bitchanges as it

counts from top to bottom.

Itcannotbe usedin arithmetic.

Itis usedin adigital system where asingle movementis critical.


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Grey CodeBIN GREY CODE BIN GREY CODE

0000 0000 1000 1100

0001 0001 1001 1101

0010 0011 1010 1111

0011 0010 1011 1110

0100 0110 1100 10100101 0111 1101 1011

0110 0101 1110 1001

0111 0100 1111 1000


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Grey Code Question:-

Change the followingdecimal numberintogrey code

12

21

11

99


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BasicGates and Function AND,

OR,

NOT,

NAND,

NOR, XOR,

XNOr,


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Sample Questions


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Sample Questions


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Sample Questions


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Sample QuestionsGive a resultof following question:

1. $AAAND $55 =

2. $0F OR $AA=

3. $C5 EOR $33 =

4. $E3 NOR 32 =


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More Sample Questions1. The correcthexadecimal equivalent for 11001010

011110012 is ___________.

2. How many binary digits make up a byte?___________.

3. How many bytes are in hexadecimal numberCBD927? _____________.

4. The uppercase Q has an ASCIIcode of1010001,

whatare the octaland hexadecimal equivalents?__________8 (octal)and __________16(Hex).

5. The weigh ofMSB ofa 6 bitbinary number is__________.


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More6. Each hexadecimaldigitconverts to

__________ binary digits.

7. In BCD, the decimal number 25 converts to________digits.

8. Even parity, means thatthe byte containsan _________ number ofones.

9. Convert110011012 toits decimalequivalent. __________ .

10. The decimalvalue for EC16 is __________.

3 digital representation

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