1. A check key that (a) consists of a single digit, (b) is appended to a data item, (c) usually is derived from the item, and (d) is used to detect errors in the item. 2. A digit that (a) is derived from and appended to digital data items and (b) can be used to detect errors in processing or in transmitting the data items. Note 1: Check digits are usually transmitted over data transmission channels. Note 2: An example of a check digit is a 7 for the numeral 106242370. The sum of the digits in the numeral is 25. The sum of the digits in 25 is 7. If the digits of the numeral are summed, modulo 9, the result is 7 again. Also, the sum of the four digits from the left is 9, the next three digits sum to 9, and only 7 and 0 remain, which, when summed, is 7. Thus, “casting out nines” is a modulo-9 check. The 7 could then be appended to the numeral as a check digit at a specified position when transmitted or stored and used to check reception or retrieval. The check digit could be appended to any specified group of numerals or digitized letters to ensure a high probability of accurate reception. Arithmetic operations may also be checked using check digits for the operands and results and performing the same operations on the check digits as on the operands. Thus, 544 × 496 = 269,824. The modulo-9 check, i.e., casting out nines, digits are 4 and 1 for the operands. Their product is 4. The modulo-9 check for the product of the operands is also 4, i.e., the sum of the digits excluding the 9 is 22, the sum of these digits is also 4. See also append,  arithmetic operation,  channel,  digit,  check,  check key,  data item,  data transmission,  detection,  digit,  error,  error detection,  key,  modulo-n check,  numeral,  operand,  operation,  overhead information,  parity check,  position,  processing,  product,  reception,  result,  specify,  store,  sum,  transmit.