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CODES. ICS 30/CS 30. BINARY CODES. Electronic digital systems use signals that have two distinct values and circuit elements that have two stable states.

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codes

CODES

ICS 30/CS 30

binary codes
BINARY CODES
  • Electronic digital systems use signals that have two distinct values and circuit elements that have two stable states.
  • A binary number of n digits, for example, may be represented by n binary circuit elements, each having an output signal equivalent to a 0 or a 1.
  • Any discrete element of info. Distinct among a group of quantities can be represented by a binary code.
    • Ex. Red is one distinct color of the spectrum.

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binary codes1
BINARY CODES
  • A bit, by defn., is a binary digit.
  • Binary codes for decimal digits require a minimum of four bits.
  • Numerous different codes can be obtained by arranging four or more bits in ten distinct possible combinations.

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slide4

Decimal

digit

(BCD)

8421

Excess-3

84-2-1

2421

(Biquinary)

5043210

0

0000

0011

0000

0000

0100001

1

0001

0100

0111

0001

0100010

2

0010

0101

0110

0010

0100100

3

0011

0110

0101

0011

0101000

4

0100

0111

0100

0100

0110000

5

0101

1000

1011

1011

1000001

6

0110

1001

1010

1100

1000010

7

0111

1010

1001

1101

1000100

8

1000

1011

1000

1110

1001000

9

1001

1100

1111

1111

1010000

Binary Codes for the decimal digits

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binary codes2
BINARY CODES
  • It is possible to assign weights to the binary bits according to their positions.
    • BCD code, 84-2-1, 2421, 5043210
    • Weighted codes
  • Numbers are represented in digital computers either in binary or in decimal through a binary code.

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binary codes3
BINARY CODES
  • The input decimal numbers are stored internally in the computer by means of a decimal code.
  • Each decimal digit requires at least four binary storage elements. The decimal numbers are converted to binary when arithmetic operations are done internally w/ numbers represented in binary.
  • It is also possible to perform arithmetic operations directly in decimal w/ all numbers left in a coded form throughout.

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binary codes4
BINARY CODES
  • Example: (395)10 when converted to binary, is equal to 110001011 and consists of nine binary digits.
  • The same number, when represented internally in the BCD code, occupies four bits for each decimal digit, for a total of 12 bits: 001110010101.
  • The first 4 bits represent a 3, the next 4 a 9, and the last 4 a 5.

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binary codes5
BINARY CODES
  • It is very important to understand the difference between conversion of a decimal number to binary and the binary coding of a decimal number.
  • In each case the final result is a series of bits.
  • The bits obtained from conversion are binary digits.
  • The bits obtained from coding are combinations of 1’s and 0’s arranged according to the rules of the code used.

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binary codes6
BINARY CODES
  • The BCD code, for example, has been chosen to be both a code and a direct binary conversion, as long as the decimal numbers are integers from 0 to 9.
  • For numbers greater than 9, the conversion and the coding are completely different.
  • Example: The binary conversion of decimal 13 is 1101; the coding of decimal 13 with BCD is 00010011.

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binary codes7
BINARY CODES
  • BCD code is the most natural to use and is indeed the one most commonly encountered
  • Excess-3, 2421, and the 84-2-1 are self complementary codes, that is, the 9’s complement of the decimal number is easily obtained by changing 1’s to 0’s and 0’s to 1’s.
  • Example: (395)10 is represented in the 2421 code by 001111111011. Its 9’s complement 604 is represented by 110000000100, which is easily obtained from the replacement of 1’s by 0’s and 0’s by 1’s.

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binary codes8
BINARY CODES
  • The biquinary code is an example of a seven-bit code w/ error-detection properties.
  • Each decimal digit consists of five 0’s and two 1’s placed in the corresponding weighted columns.
  • The error-detection property of this code may be understood if one realizes that digital systems represent binary 1 by one distinct signal and binary 0 by a second distinct signal.
  • During transmission of signals from one location to another, an error may occur.

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binary codes9
BINARY CODES
  • One or more bits may change value.
  • A circuit in the receiving side can detect the presence of more (or less) than two 1’s and, if the received combination of bits does not agree with the allowable combination, an error is detected.

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binary codes10
BINARY CODES
  • Error-Detection Codes
    • Binary information, be it pulse-modulated signals or digital computer input or output, may be transmitted through some form of communication medium such as wires or radio waves.
    • Any external noise introduced into a physical communication medium changes bit values from 0 to 1 or vice versa.
    • An error-detection code can be used to detect errors during transmission.
    • The detected error cannot be corrected, but its presence is indicated.

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binary codes11
BINARY CODES
  • A parity bit is an extra bit included w/ a message to make the total number of 1’s either odd or even.
  • During transfer of info. from one location to another, the parity bit is handled as follows: In the sending end, the message is applied to a “parity-generation” network where the required P bit is generated.
  • The message, including the parity bit, is transferred to its destination.

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binary codes12

(a) Message

P (odd)

(b) Message

P (even)

0000

1

0000

0

0001

0

0001

1

0010

0

0010

1

0011

1

0011

0

0100

0

0100

1

0101

1

0101

0

0110

1

0110

0

0111

0

0111

1

1000

0

1000

1

BINARY CODES

PARITY-BIT GENERATION

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binary codes13

1001

1

1001

0

1010

1

1010

0

1011

0

1011

1

1100

1

1100

0

1101

0

1101

1

1110

0

1110

1

1111

1

1111

0

BINARY CODES

PARITY-BIT GENERATION

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binary codes14
BINARY CODES
  • In the receiving end, all incoming bits are applied to a “parity-check” network to check the proper parity adopted.
  • An error is detected if the checked parity does not correspond to the adopted one.
  • The parity method detects the presence of one, three, or any odd combination of errors.
  • An even combination is undetectable.

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binary codes15
BINARY CODES
  • Reflected Code(also known as the Gray code)

Digital systems can be designed to process data in discrete form only. Many physical systems supply continuous output data. These data must be converted into digital or discrete form before they are applied to a digital system.

Advantage:

A number in the reflected code changes by only one bit as it proceeds from one number to the next.

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slide19

Reflected Code

Decimal Equivalent

0000

0

0001

1

0011

2

0010

3

0110

4

0111

5

0101

6

0100

7

1100

8

BINARY CODES

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binary codes16

1101

9

1111

10

1110

11

1010

12

1011

13

1001

14

1000

15

BINARY CODES

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binary codes17
BINARY CODES
  • Alphanumeric Codes

Many applications of digital computers require the handling of data that consist not only of numbers, but also of letters.

An alphanumeric code is a binary code of a group of elements consisting of the 10 decimal digits, the 26 letters of the alphabet, and a certain number of special symbols such as $.

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binary codes18
BINARY CODES
  • The total number of elements in an alphanumeric group is greater than 36. Therefore, it must be coded with a minimum of 6 bits (26 = 64, but 25 = 32 is insufficient).
  • One possible arrangement of a 6-bit alphanumeric code is shown in the table under the name “internal code.” The need to represent more than 64 characters gave rise to 7- and 8- bit alphanumeric codes. One such code is known as ASCII. Another is known as EBCDIC.

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alphanumeric character codes

Character

6-Bit internal code

7-Bit ASCII code

8-Bit EBCDIC code

12-Bit card code

A

010 001

100 0001

1100 0001

12,1

B

010 010

100 0010

1100 0010

12,2

C

010 011

100 0011

1100 0011

12,3

D

010 100

100 0100

1100 0100

12,4

E

010 101

100 0101

1100 0101

12,5

F

010 110

100 0110

1100 0110

12,6

G

010 111

100 0111

1100 0111

12,7

ALPHANUMERIC CHARACTER CODES

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alphanumeric character codes1

H

011 000

100 1000

1100 1000

12,8

I

011 001

100 1001

1100 1001

12,9

J

100 001

100 1010

1101 0001

11,1

K

100 010

100 1011

1101 0010

11,2

L

100 011

100 1100

1101 0011

11,3

M

100 100

100 1101

1101 0100

11,4

N

100 101

100 1110

1101 0101

11,5

O

100 110

100 1111

1101 0110

11,6

P

100 111

101 0000

1101 0111

11,7

ALPHANUMERIC CHARACTER CODES

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alphanumeric character codes2

Q

101 000

101 0001

1101 1000

11,8

R

101 001

101 0010

1101 1001

11,9

S

110 010

101 0011

1110 0010

0,2

T

110 011

101 0100

1110 0011

0,3

U

110 100

101 0101

1110 0100

0,4

V

110 101

101 0110

1110 0101

0,5

W

110 110

101 0111

1110 0110

0,6

X

110 111

101 1000

1110 0111

0,7

Y

111 000

101 1001

1110 1000

0,8

Z

111 001

101 1010

1110 1001

0,9

ALPHANUMERIC CHARACTER CODES

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alphanumeric character codes3

0

000 000

011 0000

1111 0000

0

1

000 001

011 0001

1111 0001

1

2

000 010

011 0010

1111 0010

2

3

000 011

011 0011

1111 0011

3

4

000 100

011 0100

1111 0100

4

5

000 101

011 0101

1111 0101

5

6

000 110

011 0110

1111 0110

6

7

000 111

011 0111

1111 0111

7

8

001 000

011 1000

1111 1000

8

9

001 001

011 1001

1111 1001

9

ALPHANUMERIC CHARACTER CODES

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alphanumeric character codes4

Blank

110 000

010 0000

0100 0000

No punch

.

011 011

010 1110

0100 1011

12,8,3

(

111 100

010 1000

0100 1101

12,8,5

+

010 000

010 1011

0100 1110

12,8,6

$

101 011

010 0100

0101 1011

11,8,3

*

101 100

010 1010

0101 1100

11,8,4

)

011 100

010 1001

0101 1101

11,8,5

-

100 000

010 1101

0110 0000

11

/

110 001

010 1111

0110 0001

0,1

,

111 011

010 1100

0110 1011

0,8,3

=

001 011

011 1101

0111 1110

8,6

ALPHANUMERIC CHARACTER CODES

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12 bit card code
12-BIT CARD CODE

When discrete info. is transferred through punch cards, the alphanumeric characters use a 12-bit binary code.

  • A punch card consists of 80 columns and 12 rows - in each column an alphanumeric character is represented by holes punched in the appropriate rows. A hole is sensed as a 1 and the absence of a hole is sensed as a 0.
  • The 12 rows are marked, starting from the top, as the 12, 11, 0, 1, 2,…,9 punch. The first 3 are called the zone punch and the last 9 are called the numeric punch.

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binary codes19
BINARY CODES
  • Most computers translate the input code into an internal 6-bit code. As an example, the internal code representation of the name “John Doe” is:

100001 100110 011000 100101 110000

J O H N blank

  • 010100100110 010101

D O E

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