1. The number which, added to the given n-digit number in radix r, results in ${\displaystyle r^{n}-1}$. In binary (${\displaystyle r=2}$), this is the ones' complement; in decimal (${\displaystyle r=10}$), this is the nines' complement.
The diminished radix complement of ${\displaystyle 01100101_{2}}$ is ${\displaystyle 10011010_{2}}$.
The diminished radix complement of ${\displaystyle 138053_{10}}$ is ${\displaystyle 861946_{10}}$.
The diminished radix complement of ${\displaystyle 0423102_{5}}$ is ${\displaystyle 4021342_{5}}$.