Please, guide me how to convert 623489base 10 to base 16

- Loser66

Please, guide me how to convert 623489base 10 to base 16

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- anonymous

Find the biggest power of 16 smaller than 623489 to determine the number of digits and just repeatedly subtract... it's like Euclidean division algorithm

- Loser66

you mean I have to go backward from biggest power of 16, not start from 16^0?

- Loser66

so 16^4 = 65536 then?

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## More answers

- anonymous

Yes

- Loser66

then?

- phi

you need a bigger number

- phi

623489 is much bigger than 16^4

- Loser66

yes

- Loser66

I need more,please, next step?

- phi

find the n so that 16^n is the first power of 16 bigger than your number
then find 16^(n-1)
divide 16^(n-1) into your number. the quotient will be the nth digit in your base 16 number. (use A for 10, B for 11, etc if you have to)
now do the same thing for the remainder

- Loser66

I got 136*(16^3) +4096 is the next number after 1*(16^4) but how to express 136(16^3)?

- phi

16^5 is bigger than your number, so 16^4 is what you divide into your number

- phi

I was under the impression that 623489 was bigger than 16^5, but it is not...

- anonymous

Yeah phi it's most certainly not

- Loser66

|dw:1371506371646:dw|then? how to express it?

- eSpeX

\(16^0=1\)
\(16^1=16\)
\(16^2=256\)
\(16^3=4096\)
\(16^4=65536\)
\(16^5=1048576\)

- phi

how are you getting 1 for the highest digit.
what do you get for
623489/16^4

- Loser66

I don't understand your question

- phi

how many times does 16^4 go into 623489 ?

- e.mccormick

1 would be the lowest didget. Sounds like you did remainder method backwards.

- Loser66

9

- phi

the idea is your number is
a*16^4 + b* 16^3 + c*16^2 + d*16^1 + e*16^0
a is 9
now subtract 9*16^4 from your number to get the remainder

- eSpeX

So 623489-(9*16^4) give you the remainder that you move to your next power.

- Loser66

got it, thank you

- Loser66

9(16^4) + 33665 and repeat the step with 33665, right?

- eSpeX

Right

- Loser66

8(16^3) +...
so, if the number before 16^ ... is bigger than 10, for example if it is 13 *(16^2) use A,B ... right?

- phi

yes,

- Loser66

got it, thanks everybody

- phi

but you should not be getting any digits > 10 for this problem

- e.mccormick

Want to see the remainder method for doing this?

- Loser66

yes

- Loser66

I searched but they give me available answer , not method.

- Loser66

my prof taught me calculate from base^0 and up. so I don't know this method

- e.mccormick

\(\cfrac{623489}{16}=38968\) with a remainder of 1
\(\cfrac{38968}{16}=2435\) with a remainder of 8
\(\cfrac{2435}{16}=152\) with a remainder of 3
\(\cfrac{152}{16}=9\) with a remainder of 8
\(\cfrac{9}{16}=0\) with a remainder of 9
If any remainder was over 9, you would need to convert to the proper letter.
Take the remaioners in reverse order: 98381

- Loser66

ok, I know this method, mod(16) and consider the remainder only.

- Loser66

quite easier than go from 16^...

- e.mccormick

Mathematically, they are related. The remainder method works in reverse, so some people like the power method better because it works the same way they would write out the number.

- eSpeX

It is also easier to use a calculator with. :)

- Loser66

@eSpeX no calculator, need method.XD

- e.mccormick

They are pretty close in calculator utility. You have to keep track of fractional values and make them into a useful number either way.

- Loser66

98381 is the answer. I gooooot it hehehe

- Loser66

@e.mccormick you explain me more about the remainder you talked. please

- Loser66

for the first one (remainder 1) the quotient is not an exponent of 16, right? how to link to the problem?

- e.mccormick

You are dividing out all possible values of 16, the SECOND digit. The remainder of this process is 1, the first digit.
So you get 38968.0625 or 38968 with a remainder of 1. That makes 1 the last digit.
Now, from 38968 you divide again. This divides out all possible instances of the third digit and leaves a remainder of the second. So on ans do forth. If I used % to mean get the mod, this becomes:
\(\cfrac{623489}{16}=38968\) & \(623489\% 16=1\)
\(\cfrac{38968}{16}=2435\) & \(38968\% 16=8\)
\(\cfrac{2435}{16}=152\) & \(2435\% 16=3\)
\(\cfrac{152}{16}=9\) & \(152\% 16=8\)
\(\cfrac{9}{16}=0\) & \(9\% 16=9\)

- Loser66

you are wicked!! I "hate" the way you do it!pal

- Loser66

and if the remainder is 10 use A, 11 use B, right?

- e.mccormick

All I am doing is keepting track of the whole part and the remainder. The whole part goes to the next digit. The remainder goes to the answer.
Yes. A=10, B=11, C=12, D=13, E=14, and F=15.

- e.mccormick

This system also works for base 8, 4, 2, and so on.

- Loser66

thank you

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