Gray encoding of decimal numbers ensures that only one bit changes when the decimal number changes by one unit. Let b₁b₂b₃ ... b_n represent an ordinary bi nary representation of a decimal number, with b₁ being the most significant bit. Let the corresponding Gray code bits be g₁g₂g₃ ... g_n. Then the Gray code representation is obtained by the algorithm 

g₁ = b₁ 

g_n = b_n ⊕ b_n-1

where ⊕ denotes modulo-2 addition (i.e., 0 ⊕ 0 = 0, 0 ⊕ 1 = 1, 1 ⊕ 0 = 1, and 1 ⊕ 1 = 0). Find the Gray code representation for the decimal numbers 0 through 32.