A similar method can be used to perform the reverse translation, but the computation of each bit depends on the computed value of the next higher bit so it cannot be performed in parallel. Assuming is the th Gray-coded bit ( being the most significant bit), and is the th binary-coded bit ( being the most-significant bit), the reverse translation can be given recursively: , and . Alternatively, decoding a Gray code into a binary number can be described as a prefix sum of the bits in the Gray code, where each individual summation operation in the prefix sum is performed modulo two.
A similar method can be used to perform the reverse translation, but the computation of each bit depends on the computed value of the next higher bit so it cannot be performed in parallel. Assuming is the th Gray-coded bit ( being the most significant bit), and is the th binary-coded bit ( being the most-significant bit), the reverse translation can be given recursively: , and . Alternatively, decoding a Gray code into a binary number can be described as a prefix sum of the bits in the Gray code, where each individual summation operation in the prefix sum is performed modulo two.