Calculate Base-k Digit Sum

Name: Calculate Base-k Digit Sum
Author: Jürgen Kummer

Calculator for the the multi-digit base-k digit sum for one or more numbers. It also calculates the alternating base-k digit sum, which alternately adds and subtracts the values. The base-k digit sum involves adding sequences of digits of length k. For instance, if k is 2, the sequences consist of two-digit numbers. Thus, the base-k digit sum is the total of these k-digit sequences, calculated starting from the right. Only digits are processed, all other characters are ignored. The String of digits output shows the value used to determine the base-k digit sum, essentially the text reduced to numbers. Single values lists the specific values used in the calculation. For a base-2 digit sum, these are two-digit values,though the final value may be a single digit.
For Weighting sequence, you can enter a sequence of weights, multiple values separated by spaces, such as 1 2 3, to specify the weight assigned to each individual value. If the field is empty or contains invalid input, a weight of 1 is assumed, meaning all values are weighted equally. The weighting is displayed alongside the individual values as a multiplier.

Examples:
the base-2 digit sum of 12345 = 45+23+1 = 69
the alternating base-2 digit sum of 12345 = 45-23+1 = 23

If a number is divisible without remainder by 101, then the same is true for its alternating base-2 digit sum and vice versa.

With the standard, non-alternating digit sum, the order of the digits does not matter. However, for a k-digit sum where k>1, the order is significant. For instance, the number 234567 has a 2-digit sum of 135, whereas 765432 has a sum of 162. This is because not only is the sequence of digit pairs reversed, but the order of the two digits within each pair is also swapped. The 23 in the first case becomes 32 in the second case. Consequently, a k-digit sum can be used as a verification method in scenarios where the order of digits matters.

Last updated on 08/25/2026. Author: Jürgen Kummer