Binary codes are codes which are represented in binary system with modification from the original ones. There are two types of binary codes: Weighted codes and Non-Weighted codes. BCD and the 2421 code are examples of weighted codes. In a weighted code, each bit position is assigned a weighting factor in such a way that each digit ca n be evaluated by adding the weight of all the 1’s the in coded combination.

**BINARY CODES **

Binary codes are codes which are
represented in binary system with modification from the original ones. There
are two types of binary codes: Weighted codes and Non-Weighted codes. BCD and
the 2421 code are examples of weighted codes. In a weighted code, each
bit position is assigned a weighting factor **in such a way
that each digit ca n be evaluated by adding the weight of all the 1’s **the in coded**
**combination.

**·** **Weighted Binary Systems**

ü
**8421 **** code/BCD cod****e **

The BCD (Binary Coded
Decimal) is a straight assignment of the binary equivalent. It is possible to assign weights to the binary bits according
to their positions. The weights in the
BCD code are 8,4,2,1.

**Example: **The bit
assignment 1001, can be seen by its weights to represent the decimal 9** **because
1x8+0x4+0x2+1x1 = 9

**Weighted
Code**

**–
**8421
code

•
**Most common **

•
**Default **

•
**The corresponding decimal digit
is determined by adding the
weights associated with t **

code
group.

**– **62310 = 0110 0010 0011**
**

**– 2421, 5421,7536, etc… codes **

**•
The wei**ghts associated with the bits in each code group are given by
the name of the code

**Nonweighted
Codes**

**–
**2-out-of-5

Non Weighted codes are codes that are not positionally
weighted. That is, each position within the binary number is not assigned a
fixed value.

•
**Actually weighted 74210 except for
the digit 0 **

•
**Used by the post office for
scanning bar codes for zip codes **

•
**Has error detection properties **

**ü** **2421 code**

This is a weighted code; its weights are 2, 4, 2 and
1. A decimal number is represented in 4-bit form and the total four bits weight
is 2 + 4 + 2 + 1 = 9. Hence the 2421 code represents the decimal numbers from 0
to 9.

ü
**5211 code **

This is a weighted code; its
weights are 5, 2, 1 and 1. A decimal number is represented in 4-bit form and
the total four bits weight is 5 + 2 + 1 + 1 = 9. Hence the 5211 code represents
the decimal numbers from 0 to 9.

ü
**Reflective code **

A code is said to be reflective
when code for 9 is complement for the code for 0, and so is for 8 and 1 codes,
7 and 2, 6 and 3, 5 and 4. Codes 2421, 5211, and excess-3 are reflective,
whereas the 8421 code is not.

ü
**Sequential code **

The BCD (Binary Coded
Decimal) is a straight assignment of the binary equivalent. It is possible to assign weights to the binary bits according
to their positions. The weights in the
BCD code are 8,4,2,1.

ü
**Excess-**** 3 cod****e **

Excess-3 is a non
weighted code used to express decimal numbers. The code derives its name from
the fact that each binary code is the corresponding 8421 code plus 0011(3).

**Example: **** **1000 of 8421 = 1011 in **Excess**-3

ü
**Gray code **

The gray code belongs to a class
of codes called minimum change codes, in which only one bit in the code changes
when moving from one code to the next. The Gray code is non-weighted code, as
the position of bit does not contain any weight. In digital Gray code has got a
special place.

**Decimal Binary Code Gray Code**

**Number**

0 0000 0000

1 0001 0001

2 0010 0011

3 0011 0010

4 0100 0110

5 0101 0111

6 0110 0101

7 0111 0100

8 1000 1100

9 1001 1101

10 1010 1111

11 1011 1110

12 1100 1010

13 1101 1011

14 1110 1001

15 1111 1000

The gray code is a reflective
digital code which has the special property that any two subsequent numbers
codes differ by only one bit. This is also called a unit-distance code.

Important when an analog quantity
must be converted to a digital representation. Only one bit changes between two
successive integers which are being coded.

ü
**Error Detecting and Correction Codes **

·
**Error detecting **** code****s **

When data is
transmitted from one point to another, like in wireless transmission, or it is
just stored, like in hard disks and memories, there are
chances that data may get corrupted. To
detect these data errors, we use special
codes, which are error detection codes.

·
**Error correcting code **

Error-correcting codes not only
detect errors, but also correct them. This is used normally in Satellite
communication, where turn-around delay is very high as is the probability of
data getting corrupt.

·
**Hamming codes **

Hamming code adds a minimum
number of bits to the data transmitted in a noisy channel, to be able to
correct every possible one-bit error. It can detect (not correct) two-bit
errors and cannot distinguish between 1-bit and 2-bits inconsistencies. It
can't - in general - detect 3(or more)-bits errors.

·
**Parity codes **

**A parity bit is an
extra bit included with a message to make the total number of 1’s either **parity
codes, every data byte, or nibble (according to how user wants to use it) is
checked if they have even number of ones or even number of zeros. Based on this
information an additional bit is appended to the original data. Thus if we
consider 8-bit data, adding the parity bit will make it 9 bit long.

At the receiver side, once again
parity is calculated and matched with the received parity (bit 9), and if they
match, data is ok, otherwise data is corrupt.

**Two types of parity**

**-Even parity: **Checks if
there is an even number of ones; if so, parity bit is zero. When the number of**
****one’s**is odd
then parity bit is set to 1.

**-Odd Parity: **Checks if
there is an odd number of ones; if so, parity bit is zero. When the number of**
****one’s**is even
then parity bit is set to 1.

ü
**Alphanumeric **** code****s **

The binary
codes that can be used to represent all the letters of the alphabet, numbers and
mathematical symbols, punctuation marks, are known as alphanumeric codes or character codes. These codes enable us to interface the
input-output devices like the keyboard,
printers, video displays with the computer.

·
**ASCII codes **

Codes to handle alphabetic and
numeric information, special symbols, punctuation marks, and control
characters.

**• ASCII (American Standard Code
Information **Interchange) is the best known.

**• Unicode –**a 16-bit
coding system provides for foreign languages, mathematical symbols, geometrical**
**shapes,
dingbats, etc. It has become a world standard alphanumeric code for
microcomputers and computers. It is a 7-bit code representing 2^{7} = 128
different characters. These characters represent 26
upper case letters (A to Z), 26 lowercase letters (a to z), 10
numbers (0 to 9), 33 special characters
and symbols and 33 control characters.

·
**EBCDIC **** code****s **

EBCDIC stands for Extended Binary
Coded Decimal Interchange. It is mainly used with large computer systems like
mainframes. EBCDIC is an 8-bit code and thus accommodates up to 256 characters.
An EBCDIC code is divided into two portions: 4 zone bits (on the left) and 4
numeric bits (on the right).

**Example 1: Give the binary, BCD, Excess-3, gray
code representations of numbers: 5,8,14.**

**Example 2: Binary To Gray Code Conversion**

**Example 3: Gray Code To Binary Code Conversion**

**Ref: **1)** ****A.P Godse & D.A Godse “Digital Electronics”, Technical publications, Pune, Revised **edition, 2008. Pg.No:31-57.

2) Morris Mano M. and Michael D. Ciletti, **“Digital Design”, IV Edition, Pearson Education**

2008.Pg.No:17-24

3) **John F. Wakerly, “Digital Design Principles and Practices”, Fourth Edition, Pearson Education **Pg.No:44-60.

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Digital Principles and System Design : Boolean Algebra and Logic Gates : Binary codes |

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