# Ace Test Series: Digital Logic - Number System

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edited
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Is it B?
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I am getting (261) base [email protected] are you getting exactly 251?
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Got it now
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the ans is b.
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266+1 ≠ 267. As it is base=7 so the digits can't be >=7.

So 7 has to be written in base 7 form which is

 71 70 1 0

i.e. 10. sum=0 and carry=1.

Again 6+1(carry) = 10 => sum=0 and carry=1

2+1=3 sum=3 carry=0

So, 266+1 = (300)7

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thanx #MiNiPanda
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Thanks for the explanation
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Shubham Aggarwal  Do let me know if you can understand this

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Best explanation....

## 1 Answer

3 votes

Best answer
$[507]_{9} 8's$ complement $=888-507=[381]_{9}=[316]_{10}=[474]_{8}$=P

$[400]_{7} 7''s$ complement$=[223]_{8}$=Q

by subtracting q from p we get $[251]_{8}$

edited by
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(400)7 =(223)8 how are you getting this plz explain.?
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(r-1)'s complement=$[666-400]_{7}=[266]_{7}$ but we need 7's complement so add 1 to the 266+1=$[300]_{7}$=$[147]_{10}$=$[223]_{8}$

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