Gray Code

Abstract

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Binary in Gray Code	Decimal
$000$	$0$
$001$	$1$
$011$	$2$
$010$	$3$
$110$	$4$
$111$	$5$
$101$	$6$
$100$	$7$

• Also known as Reflected Binary Code, Unit Distance Code, Minimum Error Code
• Another way of representing binary number, the Bit String is considered as Unweighted Code

Reduced bit switching operation

Only one bit is changed at any adjacent pair.

Important

Can be used to generate Karnaugh Map.

Unweighted Code

• The position of the digit doesn’t have value

Reflect and Prefix

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• A method used to generate Gray Code that maps to decimal number

Important

If we want to have the Gray code for $n$ bit, we need to first have the $n-1$-bit Gray code! This is because the $n$-bit Gray code is the reflection of the $n-1$-bit Gray code, with a prefix $0$ for first half and prefix $1$ for the second half, as shown in the diagram above.

References

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• Gray Code Explained | Gray code to Binary and Binary to Gray code Conversion - YouTube
• Gray Code - Friday Minis 162 - YouTube