However, I have a doubt on complexity on ‘converting base 10 to other base’ method mentioned above. As far as I understood from above post it is same as traditional method (which is handy to us) with same no. of steps and calculation with difference of Top-down and Bottom-up approach.
Let me illustrate with an example: Convert 100 in base 10 to base 6.
1. divide 100 by 6 (rem 4)
2. divide 16 by 6 (rem 4)
3. divide 2 by 6 (rem 2)
Answer: By reversing order (244)
On other hand with above mentioned approach
1. calculate range, check for greatest n, where n*36 <=100 (residue 100-72 = 28) (n = 2)
2. check for greatest n, where n*6 <=28 (residue 4) (n = 4)
3. check for greatest n, where n*1 <=4 (residue 0) (n = 4)
Answer: Same order (244)
I believe, above method definitely has some advantage over traditional method which I am unable to perceive. If possible please make me aware of that advantage. 🙂
The main advantage is, it can be done orally, more efficiently. It saves about 15-20 seconds there itself (more if you are good at calculating mentally). Which seems a small amount of time, I know – but add it over a dozen such minor calculations and you will end up attempting a couple of questions extra 🙂 {There is also a small advantage that it helps you to gain a better understanding of the numbers, rather than doing a mechanical calculation, but that is not a significant consideration for most people I guess…}
Hi Sir,
we know we can convert from 2 to 8 and vice versa using this technique, but how can we convert a no in base 5 to a no in base 7 without converting it first to decimal no system ??. Is there any shortcut for that. Thanks in advance.
CAT-holics 
Hi Sir
Thanks for writing this wonderful blog 🙂
However, I have a doubt on complexity on ‘converting base 10 to other base’ method mentioned above. As far as I understood from above post it is same as traditional method (which is handy to us) with same no. of steps and calculation with difference of Top-down and Bottom-up approach.
Let me illustrate with an example: Convert 100 in base 10 to base 6.
1. divide 100 by 6 (rem 4)
2. divide 16 by 6 (rem 4)
3. divide 2 by 6 (rem 2)
Answer: By reversing order (244)
On other hand with above mentioned approach
1. calculate range, check for greatest n, where n*36 <=100 (residue 100-72 = 28) (n = 2)
2. check for greatest n, where n*6 <=28 (residue 4) (n = 4)
3. check for greatest n, where n*1 <=4 (residue 0) (n = 4)
Answer: Same order (244)
I believe, above method definitely has some advantage over traditional method which I am unable to perceive. If possible please make me aware of that advantage. 🙂
The main advantage is, it can be done orally, more efficiently. It saves about 15-20 seconds there itself (more if you are good at calculating mentally). Which seems a small amount of time, I know – but add it over a dozen such minor calculations and you will end up attempting a couple of questions extra 🙂 {There is also a small advantage that it helps you to gain a better understanding of the numbers, rather than doing a mechanical calculation, but that is not a significant consideration for most people I guess…}
regards
J
Thanks for that quick reply. 🙂
Hi Sir,
we know we can convert from 2 to 8 and vice versa using this technique, but how can we convert a no in base 5 to a no in base 7 without converting it first to decimal no system ??. Is there any shortcut for that. Thanks in advance.
I’m afraid not…the trick works only between bases where one is a direct power of the other.
regards
J