How do I convert 2,000 from decimal to hexadecimal?

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- Jun 3rd 2013, 04:52 PMCivy71Conversion from decimal to hexadecimal
How do I convert 2,000 from decimal to hexadecimal?

- Jun 3rd 2013, 05:18 PMPlatoRe: Conversion from decimal to hexadecimal
USE THE WEB. See this webpage.

- Jun 3rd 2013, 06:26 PMProve ItRe: Conversion from decimal to hexadecimal
It helps if you think of the columns in your hexadecimal number as powers of 16, so your first digit will represent how many lots of $\displaystyle \displaystyle \begin{align*} 16^0 \end{align*}$, the second digit will represent how many lots of $\displaystyle \displaystyle \begin{align*} 16^1 \end{align*}$, the third digit will represent how many lots of $\displaystyle \displaystyle \begin{align*} 16^2 \end{align*}$, etc. Notice that $\displaystyle \displaystyle \begin{align*} 16^2 = 256 \end{align*}$ and $\displaystyle \displaystyle \begin{align*} 16^3 = 4069 \end{align*}$, so that means in hexadecimal your number can only have three digits.

Now notice that $\displaystyle \displaystyle \begin{align*} \frac{2000}{16^2} = 7\,\frac{208}{16^2} \end{align*}$, so your $\displaystyle \displaystyle \begin{align*} 16^2 \end{align*}$ digit is $\displaystyle \displaystyle \begin{align*} 7 \end{align*}$. You are left with $\displaystyle \displaystyle \begin{align*} 208 \end{align*}$.

Now notice that $\displaystyle \displaystyle \begin{align*} \frac{208}{16} = 13 \end{align*}$, so your $\displaystyle \displaystyle \begin{align*} 16^1 \end{align*}$ digit will have to be a $\displaystyle \displaystyle \begin{align*} d \end{align*}$ (which is the 13th digit).

Since there is no remainder, your $\displaystyle \displaystyle \begin{align*} 16^0 \end{align*}$ term has to be $\displaystyle \displaystyle \begin{align*} 0 \end{align*}$.

Therefore $\displaystyle \displaystyle \begin{align*} 2000_{10} = 7d0_{16} \end{align*}$. - Jun 3rd 2013, 07:43 PMibduttRe: Conversion from decimal to hexadecimal
Also visit the site : How to Convert from Decimal to Hexadecimal: 9 Steps

- Jun 4th 2013, 03:49 AMmarybaloghRe: Conversion from decimal to hexadecimal
below he shoe all the conversion of decimal to hexadecimal. i am also confusing about this problem thanks for solving......

- Jun 6th 2013, 11:14 PMJulian21Re: Conversion from decimal to hexadecimal
16^3 = 4096, which is too big

16^2 = 256, which is smaller than 2000, so divide 2000 by 256 - Jun 6th 2013, 11:24 PMProve ItRe: Conversion from decimal to hexadecimal
- Jun 8th 2013, 01:58 PMHallsofIvyRe: Conversion from decimal to hexadecimal
16 divides into 2600 121 times with remainder 0. That means that 2600= 121(16)+ 0.

16 divides into 121 7 times with remainder 9. That means that 121= 7(16)+ 9.

Putting those together 2600= (7(16)+ 9)(16)+ 0= 7(16)^2+ 9(16)+ 0 so 2600 base 10 is 790 base 16. - Jun 8th 2013, 08:19 PMProve ItRe: Conversion from decimal to hexadecimal
I'm not sure why you posted this, the number the OP was trying to convert was 2000, not 2600...

Also, your answer can not possibly be right, as 2000 in hexadecimal is 7d0, and 2600 is greater than this, yet you have gotten 790 in hexadecimal which is smaller... - Jun 10th 2013, 07:41 AMSorobanRe: Conversion from decimal to hexadecimal
Hello, Civy71!

Quote:

How do I convert 2,000 from decimal to hexadecimal?

There is an algorithm which no one has mentioned.

[1] Divide the number by the base. .Note the quotient and remainder.

[2] Divide the quotient by the base. .Note the quotient and remainder.

[3] Repeat step [2] until the zero quotient is attained.

[4] Readthe remainders.*up*

. . $\displaystyle \begin{array}{cccccc} 2000 \div 16 &=& 125 & \text{rem. }0 \\ 125 \div 16 &=& 7 & \text{rem. }13 \\ 7 \div 16 &=& 0 & \text{rem. }7 \end{array}\begin{array}{c}\uparrow \\ \uparrow \end{array}$

Therefore: .$\displaystyle 2000_{10} \;=\;7D0_{16}$

- Jul 19th 2013, 06:18 AMHallsofIvyRe: Conversion from decimal to hexadecimal