radix complement

The radix complement of n digit number y in radix b is defined to be b^n -y. Therefore, the radix complement of a number y is the number that when added to y causes the sum to “roll over” to n+1 digits.

The radix complement of a decimal number is known as the ten’s complement while the radix complement of a binary number is called the two’s complement.

The easiest way to calculate the radix complement of y is to add 1 to the diminished radix complement of y,  (b^n - 1) - y, so the radix complement is (b^n - 1) - y + 1.

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