Extremely important topic for Digital electronics, digital circuits, computer architecture and computer science. Full video is available on Youtube: https://youtu.be/oyOaXqx06pY

1. What is Gray Code?
Mukesh N. Tekwani
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2. What is Gray Code?
1. This code is named after Frank Gray, an American physicist and researcher at
the Bell Laboratories.
2. It is a non-weighted code – the position of the bit doesn’t carry any weight.
3. Successive code words differ in one bit only.
4. Also called minimum change code, unit-distance code, or minimum error code
5. It is called a cyclic code because successive words differ in one bit position only.
6. This code is also called self-reflecting code.
7. Used in analog-to-digital converters and for error-detection & correction.
8. Gray code will be used when we study Karnaugh maps.
9. Due to change of only one bit, switching operations reduced and power
efficient.
10. This code is not suitable for arithmetic operations.
Mukesh N. Tekwani

3. 4 bit Gray Code – Properties
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Decimal Binary Gray Code
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
• Non-
weighted
code
• Difference of
one bit in
successive
codes (or
minimum
change code)
• Self-reflecting
code

4. Gray Code As a Reflected Code
1. Suppose we have a Gray code representation of n-bits.
2. To obtain the Gray code representation of (n+1) bits, we write down the two n-
bit representations one below the other, with the second one being a mirror
image of the first.
3. We then add (append) a 0 at the beginning of every code in the first group and
a 1 at the beginning of every code in the second group.
4. The n least significant bits for
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5. 3 bit Gray Code as a Reflective Code
Mukesh N. Tekwani
Start Mirror 0s and 1s Mirror 0s and 1s
0 0 0 0 00 0 00
1 1 0 1 01 0 01
1 1 1 11 0 11
0 1 0 10 0 10
10 1 10
11 1 11
01 1 01
00 1 00
GRAYCODE
GRAYCODE
GRAYCODE