Can some one explain hexidemcial notation?

Question

I dont really understand it.

Answer 1

Hi,



Our numbers are in the decimal system (base 10), where each column as you move to the left is 10 times as much as the previous column. In the decimal system, the digits go from 0 up to 9, one less than the number system's base.



Likewise, in the hexadecimal system (base 16), each column as you move to the left is 16 times as much as the previous column. In the hexadecimal system, the digits need to go from 0 up to 15, one less than the number system's base. Since we don't have a digit to represent 10, 11, 12, 13, 14, or 15 we assign a number to represent each of those values. A = 10. B = 11. C = 12. D = 13. E = 14 and F = 15.



Columns in a hexadecimal represent 16^4, 16³, 16², 16^1 and 16^0. Those are 65536 (16^4), 4096 (16³), 256 (16²), 16 (16^1) and 1 (16^0).



So 345 base 16 is 3*256 + 4*16 + 5*1 = 768 + 64 + 5 = 837 (base 10).





D28B (base 16) is 13*4096 + 2*256 + 8*16 + 11 = 53,899 (base 10)





To convert 50,000 into hexadecimal, find the first column that is greater than 50,000 and start with the column below that. Since 16^4 is 65,536 which is too much, start with 16³ or 4096. Divide 50,000 by 4096. It goes in 12 times with a remainder of 848. For 12 a "C" will go in that column. Continue with the remainder of 848.



Now divide 848 by 16² or 256. It goes in 3 times with a remainder of 80. 3 will go in that column. Continue with the remainder of 80.



Now divide 80 by 16. It goes in 5 times with a remainder of 0. 5 will go in that column and it will be followed by a zero.



50,000 (base 10) = C350 (base 16)



I hope that helps!! :-)

Answer 2

You can think of scientific notation as a way of writing numbers in a manner that is not only very convenient for many calculations, but that also enables you to "size up" their value in general order-of-magnitude terms that might be more difficult if you just wrote out all the zeros there might be every time. Thus the number of particles in the observable universe, something of the order of 10^78 or more, would take 78 or more decimal places to write out in "regular" (non-scientific) notation. At the opposite end of the scale, the typical size of an atom (10^(-15)m) would take an awful lot (14) of zeros after the decimal point, before the first non-zero digit would appear. Your requested number, 6,000,000,000,000,000,000,000, is 6 x 10^21 or 6.0 x 10^21, if you prefer. In this case (but ONLY because the number starts with just one significant, non-zero digit --- see below), the power of 10 is 21 because "that's the number of zeros." (I'll explain below why you can't always just "count the zeros" in general.) The leading part of the number is always written as either a whole number or a decimal number 'n' lying in the range between exactly 1 and 9.9999... . (The upper limit is as close to 10 as you like, but not equal to 10. If it were 10, you'd be back at a leading number of 1 again.) I'll now divide up the discussion of the exponent of 10 into two cases: CASE A. The overall number is LARGER THAN 1. To get the number of zeros for a general number, consider the number 1,234, 567, say. That's 1.234567 x 1,000,000. Just as 10 is 10^1 and 100 is 10^2 (though that would apparently be news to an earlier responder!), the exponent of 10 for 1,000,000 is the number of zeros, that is 6. So 1,234,567 = 1.234567 x 10^6. [ Note that the advice to just "count the zeros" is too loose when the number ISN'T a pure power of 10! What you count is the number of IMPLIED zeros were you to put some number abcdefg... (each letter representing a digit) into the form a.bcdefg... x some power of 10. In practical terms, this means that you IGNORE the leading digit in any such number, then count all of the spaces lying between IT and the decimal point. THAT will give you the exponent of 10. ] CASE B. The overall number is LESS THAN 1. Now consider decimal numbers that are smaller than 1. The quantity 1/10 = 0.1, 1/10^2 = 1/100 = 0.01, 1/10^3 = 1/1000 = 0.001 etc. You'll notice that the rule for such numbers is SUBTLY DIFFERENT than for numbers greater than 1. Here, the number of zeros in the decimal expression is ONE LESS THAN the number of zeros in the power of 10 dividing the 1. Consider the effect of that on writing the number 0.001234567 in scientific notation. That number is 1.234567 x 0.001, and I've shown above that 0.001 means 1/1000 or 10^(-3). This is an example of the general rule for numbers less than 1: Count the number of zeros, 'z' beween the decimal point and the first NON-ZERO digit (In the example just given, z = 2.) Add 1 to z; here, z + 1 = 3. Then your power of 10 is - (z + 1); here, that's - 3. One more example. Consider 0.0678. There is just 1 zero; add 1 to 1, giving 2; the exponent will then be - 2; so it's 6.78 x 10^(-2). C. A PRACTICAL SUMMARY! If you've read and understood the principles explained above, there is a slightly more practical and efficient way of finding the power of 10 which corresponds to those principles: For case A. Write out the full number as a regular decimal, say it's abcdefghi.jkl... . Take the decimal point and IMAGINE moving it LEFT until it's just AFTER the leading digit 'a.' The number of places it had to be moved (in this case, 8) is the power of 10. The number is a.bcdefghijkl... x 10^8. For case B. How about 0.0000rstuv... ? Move the decimal point to the RIGHT until it's immediately after the leading non-zero digit 'r.' How many places did it move?(5, in this case.) The NEGATIVE of that number (- 5) is the needed power of 10; this number is r.stuv... x 10^(- 5). It may seem a bit confusing at first, but like everything else in mathematics, with practice you'll become much more comfortable with it. Good luck! Live long and prosper.

Answer 3

It just means you are using base 16 instead of base 10. The rightmost digit represent 1, the next one indicates 16, and the next one indicates 256, instead of 1, 10, and 100. Of course, if one digit needs to be ten or more, you run out of symbols for the digits, so you have to switch to letters: A=10, B=11, C=12, D=13, E=14, F=15. Computers use binary numbers (base 2), but they are easy to convert to and from hexadecimal, and hexadecimal numbers are easier for humans to deal with. How do you pronounce 1011100101001, or remember it? As someone else explained, the binary number can be split into groups of 4 digits, and each group can be replaced by one "hex" digit. Decimal numbers can be converted to hex, also, but it's a little harder: you divide the number by the highest power of 16, put down a digit, then divide the remainder by the next lower power of 16, and so on.

Answer 4

It has a base of 16. Our decimal system has a base of 10, so each digit can be from 0-9. But in hexadecimal, each digit can be 0-9 or A-F. A means 10, B means 11,... F means 15.



To convert from hex to decimal, multiply the right-most digit by 16^0 = 1, the next digit by 16^1 = 16, the next digit by 16^2 = 256, etc.



18C in hex = 1*256 + 8*16 + 12*1 = 396 in decimal

Answer 5

hexidecimal notation is really a "short-way" to write binary numbers

in 4-bit format.



let's say you have this no. in binary form.



111100101011001111



first thing you do is break down the binary format in four bit increments

starting from the rightmost.



0011 1100 1010 1100 1111



the leading zeroes on the leftmost is not necessary but is good practice. then convert them to decimal equivalents.



3CACF



A = 10

B = 11

C = 12

D = 13

E = 14

F = 15



good luck!