How do you compute hexadecimal numbers?

Question

Expecially how to change hexidecimal to decimal.

Answer 1

This is kind of hard to show without pencil & paper, but here are some ideas...

First, consider ordinary decimal numbers. They have the form where the first digit on the right represents ones, the next is tens, then hundreds, etc. Going right of the first digit, there are tenths, hundredths, thousandths, etc. Note that 10 is 10^1, 100 is 10^2, 1000 is 10^3, etc. And 1 is 10^0, 0.1 is 10^-1, 0.01 is 10^-2, and so on. For numbers of other bases, the same principle applies. You can make the following chart, where "n" is the base for the number system:

...n^3 n^2 n^1 n^0 . n^-1 n^-2 n^-3...

For hex, n = 16. 16^0 = 1, so the n^0 slot is for ones. 16^1 = 16, so the n^1 slot is for the sixteens. 16^2 = 256, so n^2 is for the twohundredfiftysixes. Likewise going to the right, for the numbers < zero. 16^-1 is for the sixteenths, 16^-2 is for the twohundredfiftysixths, etc.

Well, enough of the theory, for now (I'm lazy). Here's an example of how you change a hex number to a decimal. Let's convert 3C9.B to decimal: The 9 is in the ones' spot, so it has a value of 9*1 = 9. The C is in the sixteens' slot, so it's 12*16 = 192. The 3 is in the twohundredfiftysixes' slot, so it's 3*256 = 768. Going to the right, the B is in the sixteenths slot, so it's 10*(1/16) = 10/16 = 0.625.

Then you add them up: 3C9.B = 9 + 288 + 192 + 0.625 = 489.0625.

I don't THINK I made any mistakes...

Answer 2

Hex== Bin== Dec
0== 0000 ==0
1== 0001 ==1
2== 0010 ==2
3== 0011 ==3
4== 0100 ==4
5== 0101 ==5
6== 0110== 6
7== 0111== 7
8== 1000 ==8
9== 1001== 9
A ==1010== 10
B== 1011== 11
C== 1100 ==12
D== 1101 ==13
E== 1110 ==14
F ==1111 ==15



Example of conversion from hexadecimal triplet to decimal triplet: Hexadecimal triplet: FFCF4B

Separate the triplets: FF CF 4B

Convert each hexadecimal value to a decimal representation:

FF = 15*16 + 15*1 = 255
CF = 12*16 + 15*1 = 207
4B = 4*16 + 11*1 = 75
Hexadecimal triplet FFCF4B = Decimal triplet 255,207,75

Answer 3

Hexidecimal means "base 16."

Most people use a base 10 system. Whatever you use, the base is that "Unreachable" number. For example, in base 10, there is no digit for 10, you start a new column representing how many 10's you've amassed. You have a 1's column a 10's column a 100's column and so forth. To get the numerical value you multiply (most people are so used to it, they just do it in their head). If the number is 823 you can express it as 3X1 plus 2X10 plus 8X100
3x1 = 1
2x10 = 20
8X100=800
-----------------
1+20+800= 821

So 3 plus 20 plus 800. Make sense?

In binary "2" is the unreachable number, so you go 1, 10, 11, 100, etc. You have a 1's, 2's, 4's, 8's column.
The number 11011 would be 1Xone, plus 1xtwo, plus 0Xfour, plus 1xeight, plus 1x16 or 27 in base 10.

1x 1 = 1
1x 2 = 2
0x 4 = 0
1x 8 = 8
1x16 = 16
---------------
1+2+8+16=27

In Hex 16 is the unreachable number so you have numbers 1-15 expressed in the first column. Since we don't have a digits for numbers 10-15 we use lettes like for the higher values, to count 1-15 in hex it is: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, A, B, C, D, E, F. Then the "16" is 10. so you end up with a 1's column, a 16's column, a 256's column, etc.

So if you're given a number of B49 is hex you know you have 9x1 plus 4x16 plus 11x256 or 2889 is base10.

9 x 1 = 9
4 x 16 = 64
11x 256=2816
-----------------------
9+64+2816=2889


Hope that helps.

Cheers,
Odd

Answer 4

The first digit of a hexadecimal number is the number of times 1 goes into the number. The second is the number of 16's, then 256's, then 4096's, and so on.So to convert a decimal to hexadecimal, divide by 4096 or 256 or whatever is the largest power of 16 that's smaller than your number, and the result is the first number. Then divide the remainder by the next-lower power and that's the next digit. Keep going until you've divided by 16, and the remainder is the ones' digit.

To convert from hexadecimal to decimal, multiply the number in the 1's place by 1, the 16's place by 16, etc., then add the products together.

And remember, you may have to use digits inhex that don't exist in decimal. the letters A-F correspond to the "digits" 10-15.

Answer 5

When you were little, did you label the columns Units, Tens and Hundreds (Tens squared) and Thousands (Tens cubed)?

In hexadecimal the columns represent Units, Sixteens and Sixteens squared, and Sixteens cubed.

Since you need extra symbols, use the letters A to F to represent ten, eleven, twelve thirteen, fourteen and fifteen, all base 10 in base 16

12B5 in hexadecimal is

5 + 11 x 16 + 2 x 16^2 + 1 x 16^3

=5 +11 x 16 + 2 x 256 + 1 x 4096

=5 + 176 + 512 + 4096

= 4789

Answer 6

hexadecimal is just a "shorthand" way of expressing binary and uses all the bits the number takes up so its more efficient in use of memory than decimal Take number 15(decimal) this takes up 8 bits (4 bits for the 1 and four bits for the 5) However this in hexadecimal = F = just 4 bits in binary So you have used 1/2 the amount of memory required to store the number in hexadecimal than in decimal Repeat this over loads of numbers and you can save loads of memory. And its a hellova lot easier to write big numbers as hexadecimal than long strings of binary and you are FAR less likely to make mistakes in writing them (you try writing a big number represented as 32 binary bits without making a mistake compared to 8 hexadecimal characters. Then have a look what FFFFFFFF hexadecimal is in decimal, both as a number and as the number of digits in that number.)

Answer 7

They are base 16 whereas decimal is base 10. i

In hex 101 = 1*16^2 + 0*16^1 + 1*16^0

So, to go from hex to dec just multiply out all the numbers and add.

Answer 8

Use PC's calculator, change the view to Scientific, click Hex radio button and enter hex digit, click Dec radio button to see decimal number.

Answer 9

When you think of "normal" numbers, you are thinking of numbers in base 10. For example, 100 = 1*(ten)*(ten) and 1000=1*(ten)*(ten)*(ten). In hexidecimal, the base is not ten, but sixteen. so 100=1*(sixteen)*(sixteen), which is equal to 256 (base ten). To represent digits larger than nine, hexidecimal makes use of capital letters. So, for example, the digits base ten are {0,1,2,3,4,5,6,7,8,9}, but for base sixteen they are {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}
. So A7B in base sixteen = A*(sixteen)*(sixteen)+7*(sixteen)+B=(ten)*(sixteen)*(sixteen)
+7*(sixteen)+(eleven) which equals 2683 decimal. Hope this helps!