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Gray Codes

• 1-bit Gray code $G$₁

  i	G$$1(i)
  $0$	$0$
  $1$	$1$

• $n$-bit Gray code $G$_n

  i	G$$n(i)	i	G$$n(i)
  $0$	$0\; G$n-1(0)	$n-1$	$1\; G$n-1(0)
  $1$	$0\; G$n-1(1)	$n-2$	$1\; G$n-1(1)
  ...	...	...	...
  $n/2-1$	$0\; G$n-1(n/2-1)	$n/2$	$1\; G$n-1(n/2-1)

• Required properties preserved by construction!