This document describes a digital electronics project to build binary to gray code and gray to binary converters using XOR gates. A group of 4 students submitted the project to their professor. The introduction defines binary and gray codes. Gray codes differ from binary in that only one bit changes between adjacent numbers. The document explains how to calculate gray codes by XORing binary bits. It then describes the circuit built using an IC7486 XOR gate, resistors, LEDs, buttons and a power supply. The circuit converts between gray and binary codes. Finally, the document discusses the uses of these converters and concludes that the project was successfully implemented and tested.

1. DIGITAL ELECTRONICS PROJECT
BINARY TO GRAY & GRAY TO BINARY
CONVERTER USING XOR
(SUBMITTED BY)
SECTION – E1513A
 D.DINESH - (11502811)
 P.BABU RAO - (11506764)
 M.SAI - (11507762)
 P.MOHAN KRISHNA - (11507237)
(SUBMITTED TO)
shri. ABHINAV VISHNOI
ASSISTANT PROFESSOR
LOVELY PROFESSIONAL UNIVERSITY

2. INTRODUCTION
WHAT IS BINARY CODE :-
BINARY code is a way of representing the text
or the data generated by the computers and other devices .
In binary coding the text or the data is represented in a stream of bits of 1's and
0's.
that is weighted as ......8,4,2,1 . so for forming 7 , you just need 111.similar
computation for other decimal numbers .
WHAT ARE GRAY CODES:-
GRAY CODES are non weighted codes , that is
they can’t be provided a weight to calculate their equivalent in decimal . Gray
codes are often called reflected binary code , the reason is clear if you compare
the column of gray code with the binary code . gray Code is a symbolic
representation of discrete information. Codes are of different types. Gray Code
is one of the most important codes. It is a non-weighted code which belongs to a
class of codes called minimum change codes. In this codes while traversing
from one step to another step only one bit in the code group changes. In case of
Gray Code two adjacent code numbers differs from each other by only one bit.
The idea of it can be cleared from the table given below.
HOW GRAY CODES ARE CALCULATED :-

3. Here D is the M.S.B ( most significant bit ) and A is the LSB (least significant
bit ). The MSB is written as it is .for writing the other digits we XOR the inputs
binary bits to obtain the output gray code bits .
FOR example -
If I want to calculate the gray code of 0110. the following steps are performed-
1) the M.S.B is written as it is , that is 0.
2) then the M.S.B and the digit and right side of it is XOR'ed to obtain the next
digit in gray code . 0 is XOR'ed with 1, so the output next digit is 1 .
3) similarly other digits are XORed to obtain the gray code

4. GRAY TO BINAY CIRCUIT:-
COMPONENTS USED
1.BREAD BOARD
2.CONNCETING WIRES.
3.LEDS
4.IC7486(XOR).
5.RESISTORS.
6.PUSH BUTTON SWITCHES.
7.BATTERY POWER SUPPLY.
The 7486 IC package contains four independent positive logic XOR GATES.
Pins 14 and 7 provide power for all four logic gates.
Outputs of one gate can be connected to inputs of another within the same chip
or to another chip as long as they share the same ground. The figure to the left
illustrates a basic circuit showing how to wire inputs and using LEDs to display
outputs.
Use caution when wiring chip and be sure to check which pins are outputs and
inputs!
XOR GATE Logic-Rules:
The output is HIGH when one OR the other input is HIGH, but NOT both. If
both inputs are high output will be LOW.

5. Circuit diagram:-
1)TO pin number 14 Of IC 7486 Vcc is applied & pin number 7 is grounded .
2)Assemble the circuit on bread board, as per above diagram.
3) Give the logical inputs and check for the proper output, as per the truth table.

6. USES:
Binary - gray Code and gray-binary Converter is an online tool used in
digital computation to convert either Binary code into its equivalent gray code
or gray code to its equivalent Binary code. From the above, this calculator is
comprises of two converters namely Binary to gray Code Converter and gray to
Binary Code Converter and it is separated by the respective radio button.
2.the gray coding is meant for minimizing bit errors bycausing adjacent words
to only be one bit off from their neighbours. That
way, a bit of noise that's only enough to push the received signal over
by one spot in the constellation only causes a single bit error.
Contrast that with what would happen if you put '0111' next to '1000',
'0000' next to '1111', '0011' next to '1100', etc.
CONCLUSION
Integrating features of all the hardware components used have been developed
in it. Using highly advanced IC’s with the help of growing technology, the
project has been successfully implemented. Thus the project has been
successfully designed and tested.
THANKYOU