Please teach me octal and hexadecimal?

Question

^_^

Answer 1

I'm not sure anyone has "taught" you anything yet.

The "base" of a number system indicates how many different digits are used. The base also tells us the first value that will need two digits to be expressed. We normally use a base 10 numbering system--10 is the first two-digit number.

Octal is a base 8 numbering system. The numbers in octal (counting up) are 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, ... As you can see, there are only 8 different digits used in this numbering system. (By the way, the largest two-digit number in octal is 77. The next number is 100.)

Hexadecimal is a base 16 numbering system. That means that 16 must be the first value that requires two digits, so we borrow letters of the alphabet to give us enough digits. Counting up in hexadecimal looks like this:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21, 22, ...
As you keep going, you can have a value like EA--both of those are digits. The biggest two-digit number in hexadecimal is FF--the next number after that is 100.

How do we think about numbers in these other systems?

Remember that in our base 10 numbering system the first digit (on the right) is the "ones" digit, the next digit is the "tens" digit, the next is the "hundreds" digit, and so forth. Notice that these are represented as powers of the base. That is, the first digit is the 10^0 digit, so take the value here and multiply by 10^0. The next column is the 10^1 column. The next column is the 10^2 column. The next would be the 10^3 column.

The same is true in the other systems. In octal, the first digit (on the right) is the "ones" column (8^0). The next column would be the "eights" column (8^1). The next column would be the "sixty fours" column (8^2). And so forth. So the octal value 427 means that we have 4 sixty-fours, 2 eights, and 7 ones (the decimal value would be 279).

In hexadecimal, the first digit (on the right) is the "ones" column (16^0). The second digit is the "sixteens" column (16^1). The next column would be the "two hundred fifty-sixes" column (16^2). So the hexadecimal value 2AB means that we have 2 of the sixteen squares, A sixteens, and B ones (the decimal equivalent would be 683).

This doesn't give you nice neat formulas for converting (but you didn't ask for that). But does this help make sense of these numbering systems?

The reason these are used, by the way, is that they both relate nicely to the binary numbering system--which is what machines use. In binary (base 2), there are only two digits--0 and 1--on and off--so switches operate in a binary world. Instead of talking in binary, the digits are grouped. Octal corresponds to groups of three binary digits, while hexadecimal corresponds to groups of four binary digits.

Answer 2

We normally count on base 10
1 2 3 4 5 6 7 8 9 10 11..

Octal is the concept of counting on base 8.
1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20..

Hexadecimal is the notion of counting on base 16
1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12..

So 10 in octal notation is actually 8 in decimal
and 10 in hexadecimal is actually 16 in decimal
Octal and Hexadecimal are used for their easy translations in binary. I am assuming you know that one.

You can read up more about these here
http://www.learn-programming.za.net/articles_decbinhexoct.html

Answer 3

What do you want to know?

In Octal, you go

0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 .....

In Hex you go

0 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 .....

Answer 4

Octal is base 8
To convert decimal to octal, find the highest power of 8 in the number, eg in 89 it is 64. since there is 1 64 in 88 the first digit is 8. The remainder (88-64) is 25, which is 3*8+1. so the second digit is 3. the number of units left is 1. so 88 (decimal) = 131 (octal)

hex is similar, but different in that the base 16 is greater than 10. the digits used are 0123456789ABCDEF.


so if you have 300 (decimal to convert) the highest power of 16 is 256. there is one 256 in 300 so the first digit is 1. subtract to get 44. this is 16*2+11. so the second digit is 2. the third digit is the value 11, which is represented by B so 300 (decimal) = 12B (hex)

Answer 5

ok.

Hexadecimal is easy! converts to hexadecimal :

48 65 78 61 64 65 63 69 6d 61 6c 20 69 73 20 65 61 73 79 21

Answer 6

draw a square 10 x 10 using decimal numbering system.

123 45678910

123 45678910

123 45678910

123 45678910

123 45678910

123 45678910

123 45678910

123 45678910

123 45678910

123 45678910

a)so first number is 1 and the last number is 10
b)delete row 9 and column contianing 9, retaining row and column of 10, you now have numbering system with base 9
c)similarly delete rows 8 & 9 and columns contianing 8 & 9 retaining row and column of 10, you now have numbering system with base 8
d)next delete rows 4,5,6,7,8 & 9 and columns contianing 4,5,6,7,8 & 9, retaining row and column of 10, you have numbering system with base 4
f)for hexadecimal system insert rows designating as a,b,c,d,e & f and columns designating as a,b,c,d,e & f, between rows and columns of 9 & 10, you have numbering system with base 16.

best real life example for different numbering systems are
g) days of the week which uses base 7,
months of a year which uses base 12,
alphabet which can be used as base 26.
trust i have made subject clear.
you can use excel file for trying out