# Conversion from decimal to hexadecimal

• Jun 3rd 2013, 04:52 PM
Civy71
How do I convert 2,000 from decimal to hexadecimal?
• Jun 3rd 2013, 05:18 PM
Plato
Re: Conversion from decimal to hexadecimal
Quote:

Originally Posted by Civy71
How do I convert 2,000 from decimal to hexadecimal?

USE THE WEB. See this webpage.
• Jun 3rd 2013, 06:26 PM
Prove It
Re: Conversion from decimal to hexadecimal
Quote:

Originally Posted by Civy71
How do I convert 2,000 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 PM
ibdutt
Re: Conversion from decimal to hexadecimal
• Jun 4th 2013, 03:49 AM
marybalogh
Re: Conversion from decimal to hexadecimal
• Jun 6th 2013, 11:14 PM
Julian21
Re: 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 PM
Prove It
Re: Conversion from decimal to hexadecimal
Quote:

Originally Posted by Julian21
16^3 = 4096, which is too big

16^2 = 256, which is smaller than 2000, so divide 2000 by 256

Is this not exactly what I posted in my previous post?
• Jun 8th 2013, 01:58 PM
HallsofIvy
Re: 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 PM
Prove It
Re: Conversion from decimal to hexadecimal
Quote:

Originally Posted by HallsofIvy
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.

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 AM
Soroban
Re: 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.

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

Therefore: .$\displaystyle 2000_{10} \;=\;7D0_{16}$
• Jul 19th 2013, 06:18 AM
HallsofIvy
Re: Conversion from decimal to hexadecimal
Quote:

Originally Posted by Prove It
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...

One of these days, I really need to learn arithmetic!