Question

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

Answer 1

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

Answer 2

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

Answer 3

so 16^4 = 65536 then?

Answer 4

Yes

Answer 5

then?

Answer 6

you need a bigger number

Answer 7

623489 is much bigger than 16^4

Answer 8

yes

Answer 9

I need more,please, next step?

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

Yeah phi it's most certainly not

Answer 15

then? how to express it?

Answer 16

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

Answer 17

how are you getting 1 for the highest digit.


what do you get for
623489/16^4

Answer 18

I don't understand your question

Answer 19

how many times does 16^4 go into 623489 ?

Answer 20

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

Answer 21

9

Answer 22

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

Answer 23

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

Answer 24

got it, thank you

Answer 25

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

Answer 26

Right

Answer 27

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?

Answer 28

yes,

Answer 29

got it, thanks everybody

Answer 30

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

Answer 31

Want to see the remainder method for doing this?

Answer 32

yes

Answer 33

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

Answer 34

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

Answer 35

\(\cfrac{623489}{16}=38968\) 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

Answer 36

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

Answer 37

quite easier than go from 16^...

Answer 38

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.

Answer 39

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

Answer 40

@eSpeX no calculator, need method.XD

Answer 41

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

Answer 42

98381 is the answer. I gooooot it hehehe

Answer 43

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

Answer 44

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

Answer 45

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:

\(\cfrac{623489}{16}=38968\) & \(623489\% 16=1\)
\(\cfrac{38968}{16}=2435\) & \(38968\% 16=8\)
\(\cfrac{2435}{16}=152\) & \(2435\% 16=3\)
\(\cfrac{152}{16}=9\) & \(152\% 16=8\)
\(\cfrac{9}{16}=0\) & \(9\% 16=9\)

Answer 46

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

Answer 47

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

Answer 48

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.

Answer 49

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

Answer 50

thank you