Definition:Gray Code

Definition

The Gray code is a binary code designed such that successive codewords differ by $1$ bit.

Gray code

$n$	Binary	Gray
$0$	$0000$	$0000$
$1$	$0001$	$0001$
$2$	$0010$	$0011$
$3$	$0011$	$0010$
$4$	$0100$	$0110$
$5$	$0101$	$0111$
$6$	$0110$	$0101$
$7$	$0111$	$0100$
$8$	$1000$	$1100$
$9$	$1001$	$1101$
$10$	$1010$	$1111$
$11$	$1011$	$1110$
$12$	$1100$	$1010$
$13$	$1101$	$1011$
$14$	$1110$	$1001$
$15$	$1111$	$1000$

Also see

• Definition:Baudot Code

• Results about the Gray code can be found here.

Source of Name

This entry was named for Frank Gray.

Historical Note

The Gray code was invented by Frank Gray in $1947$.

A similar code, the Baudot code, had been invented in $1878$ by Émile Baudot.

The Gray code is widely used in analogue-to-digital conversion, and has very useful error-correcting properties.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Gray code