How to find 4's complement of 7 base 10 [closed]

Question

How to find 4's complement of $7_{10}$?

Approach 1: Convert to base-4 and find its radix complement

$7_{10} = (13)_4$

Radix complement(4's complement) = $21_4 = 9_{10}$ (result)

Approach 2: Convert to base-5 and find its diminished radix complement

$7_{10} = (12)_5$

Diminished radix complement (4's complement) = $(32)_5 = (17)_{10}$ (result)

Are these approaches correct? If yes, why different results?!

Comments

" diminished radix complements are called by the radix − 1 "

means diminish radix complement of 5 is base 4 of a number

right?

---

If radix/base = r  then

radix complement = r's complement  = (rⁿ)₁₀ - Number

diminished radix complement = (r-1)'s complement = (rⁿ - 1)₁₀ - Number

(rⁿ - 1)_r represents maximum number in radix/base 'r' with n digits

For example 999 is maximum 3 digit number in decimal number (base-10) system

777 is maximum 3 digit number in octal number system(base-8)

333 is maximum 3 digit number in base-4 number system..

---

yes thanks

Answer 1

Approach 1 is wrong:- First understand what we mean by b's complement (diminshed  radix complement). Take a number X  of n digit and find (bⁿ -1) and subtract X from it.

You are converting to base 4 and its diminshed radix complement will be 3's complement no. 4's complement.