Base 5

**t-lee** · October 30th 2006, 11:47 AM

Does 124(base 5) represent an odd number? How can you determine whether a number is odd by looking at its base-five representation?

Any takers?

**ThePerfectHacker** · October 30th 2006, 12:10 PM

Originally Posted by t-lee

Does 124(base 5) represent an odd number? How can you determine whether a number is odd by looking at its base-five representation?

Any takers?

$(124)_5$
Is,
$1\cdot 5^2 +2\cdot 5^1+4\cdot 1$
Is that even or odd?

**Soroban** · October 30th 2006, 02:31 PM

Hello, t-lee!

Does $124_5$ represent an odd number? . . . no

How can you determine whether a number is odd by looking at its base-five representation?

Since the base is an odd number, it could be tricky.

But there is a simple rule:
. . Even number of odd digits: even
. . .Odd number of odd digits: odd

**Quick** · October 30th 2006, 03:43 PM

Originally Posted by Soroban

Since the base is an odd number, it could be tricky.

But there is a simple rule:
. . Even number of odd digits: even
. . .Odd number of odd digits: odd

there is an odd number of odd digits in 124...

**topsquark** · October 30th 2006, 04:49 PM

Originally Posted by Quick

there is an odd number of odd digits in 124...

Yes, which means that $124_5$ is odd which, in fact, it is. Don't let that 4 on the end fool you. What TPH was trying to say is that
$1 \cdot 5^2$ is odd
$2 \cdot 5^1$ is even
$4 \cdot 5^0$ is even

odd + even + even = odd.

-Dan

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