Digital Logic : 10's Complement

Question

I can't seem to understand the 10's Complement.

10' s complement of 0 is 10 [ https://www.mathsisfun.com/numbers/tens-complement.html ]

However, The problem in Morris Mano's Digital Design

10's Complement of 00,000,000

the answer in Solution Manual is 00,000,000.

I am having a hard time understanding this. Can anyone explain this?

Comments

I think, its all about the no. of digits in the answer. 10's complement of 00,000,000 wil be 1,00,000,000.

Answer 1

Use the formula

r's complement = r ^n-N Here r is base n is number of digit and N is number which 10's complement need to get .

Comments

n would be the number of digits in 00,000,000 ? That would make it 8

so 10^8 - 0 = 10^8..

Am i missing something here ?

Answer 2

for   00,000,000   all LSB's remains as it is because no non-zero digit is encountered so answer would be  00,000,000

Source : Morris Mano

Comments

Then why 10's complement of 0 is 10 if we have to leave all the least significant zeroes untouched? Please explain..

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are u sure brother that 10's complement of 0 is 10 ? because Ive no idea about this

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I don't know..I just came to know about this from XbrucewayneX 's post

Answer 3

r's complement of an n-digit number in base r is defined as r^n-N for all N except 0.

for 0, the r's complement is 0 itself.

-Morris Mano

For finding 10's complement of a number, leave all least significant 0's unchanged, subtract first non zero least significant number from 10 and the rest of digits from 9.

Hence, for 10's complement of 00,000,000: leave all 0's unchanged. Hence the solution is: 00,000,000

Answer 4

Consider 8 bit only then 100000000 this is 10's complement of 0 but just 8 bit consider then answer is 00,000,000