# diminished radix complement

The diminished radix complement of an *n* digit number *y* in radix *b* is defined to be . Therefore, the radix complement of a number *y* is the number that when added to *y* causes the sum to be the largest possible number that can be store in *n* digits.

The radix complement of a decimal number is known as the *nines’s complement* while the radix complement of a binary number is called the *one’s complement*.

Could you explain why the diminished radix complement is b^n-1-y? I don’t think I fully understand the concept of a radix complement.

How would you find a 8’s complement of a n-digit base 10 number?

Have you read this post about Number System Complements? I am more thorough explaining them there.

Link: http://www.neuraldump.com/2017/01/number-system-complements/

Sorry for the late reply. Yes, I’ve read those articles that you wrote but I’m not sure why I decided to make the comment here. I somehow thought it was more fitting back then.

It seems that you just defined the diminished radix complement to be b^n-1-y. But when you call the diminished radix complement for a base 10 number the 9’s complement, it seems to suggest that a more general 8’s or 7’s, or perhaps even an 11’s complement would exist as well for this base 10 number.

I’ve been Googling around and I’ve found a more general definition for the diminished radix complement that includes fractional numbers as well. Following your notation, it goes like b^n-b^m-y, where n is the number of digits in the integer part and m is the number of digits after the binary point (when m=0, b^m=1). This is all usually stated without any explanation.

Here are some of the documents that I found through Google that have such a definition:

https://ece.uwaterloo.ca/~msachdev/ECE223/Overhead%20Slides/ECE%20223%20Number%20System.pdf

http://osp.mans.edu.eg/cs212/CS212_chapter_1_notes.pdf