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.
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 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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Decimal (BCD) Excess-3 84-2-1 2421 (Biquinary)
digit 8421 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
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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 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 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 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 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 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 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 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 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 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 CODES
(a) Message P (odd) (b) Message P (even)
PARITY-BIT GENERATION
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
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PARITY-BIT GENERATION
BINARY CODES
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
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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 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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BINARY CODES
Reflected Code Decimal Equivalent
0000 0
0001 1
0011 2
0010 3
0110 4
0111 5
0101 6
0100 7
1100 8
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BINARY CODES
1101 9
1111 10
1110 11
1010 12
1011 13
1001 14
1000 15
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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 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 7-Bit ASCII 8-Bit 12-Bit card
code code EBCDIC code
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
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ALPHANUMERIC CHARACTER
CODES 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
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ALPHANUMERIC CHARACTER
CODES 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
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ALPHANUMERIC CHARACTER
CODES 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
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ALPHANUMERIC CHARACTER
Blank 110 000 010 0000 0100 0000 No punch
CODES . 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
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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 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
010100 100110 010101
D O E
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