PMC

Block sum check algorithm to detect errors. a Conventional block sum check in data transmission. b Block sum check for quaternary digit data (DNA)

Calculation of the check digit of the PIN. Each digit in the PIN is multiplied by 2 or 1 in alternating fashion. The products are summed up, but products consisting of two digits (*) are first summed up themselves (i.e. 12 = 1 + 2 = 3). In this case, the sum of products treated this way, is 36. # The last digit in the product sum (in this case 6) is extracted from 10 (the difference being “4”). If the product sum ends with “0” (e.g. 10, 20, 30, 40 etc.), the check digit “0” is assigned since “10” cannot function as the check digit

Block sum check algorithm of the encrypted DNA sequence. a Three information types (developer, taxonomy, and version) were encrypted from plain text into the DNA sequence according to the encryption table (Table ). “9606” denotes Homo sapiens. The nucleotide sequence was then arranged in 2D. b For block sum check, nucleotides were changed to quaternary digit numbers (A = 0, T = 1, G = 2, C = 3). For each row, the sum of the numbers was divided by 4, and the remainder was then converted to a nucleotide. For example, the sum of the first row was divided by 4, and its remainder was 2. This 2 was then converted to a corresponding nucleotide, G. For each column, the same process was iterated to obtain parity nucleotides. c The parity nucleotides for error check are shown in red color. d The final 1D sequence of encrypted and mutation-detectable sequence was constructed

Grey boxes represent dead branches where no corresponding mark was found in the codeword (note that check sum bits are not represented here to aid with clarity).