Can any one give me information on the Denary System.?

Question

Such as, how it began and who it started with?

Answer 1

The Denary Number System
The ten-digit, or denary number system, is an arbitrary system that we have all agreed to use because it makes sense to us. The denary system is based on 10 digits (0-9) and is therefore said to have a base of 10, or base 10. A car's odometer can help visualize what goes on when we count in base 10. As a car puts on more miles, the odometer's miles increase. On the 10th mile we run out of numbers to put in the ones column, so the column holding the tens is incremented by one and the ones column starts over again. After 99 miles, the column holding the hundreds is incremented by one and both the ones and tens columns start over again. Or, to be more explicit, consider the following number:
1946

Reading from right to left, the 6 is in the ones column, the 4 is in the tens column, the 9 is in the hundreds column, and the 1 is in the thousands column. This number can also be represented as

[(6 * 100) + (4 * 101) + (9 * 102) + (1 * 103)] =
(6 + 40 + 900 + 1000) =
1946.

Note that all the numbers are multiplied by a power of the base (100, 101, 102, etc.). In this page, I use the asterisk (*) to represent multiplication, e.g., 4 * 3 = 12.

The Binary Number System
Computers, on the other hand, have only two fingers to count with, On and Off. Hence computers speak in a binary language of 0s and 1s. What would a car odometer do if it were using a binary system? Instead of flipping on powers of 10, it would flip on powers of 2. Let's again consider the number 1946. In a binary system, this number can only be represented with ones and zeros, so it translates to 11110011010, or
[(0 * 20) + (1 * 21) + (0 * 22) + (1 * 23) + (1 * 2 4) + (0 * 25) + (0 * 26) + (1 * 27) + (1 * 28) + (1 * 29) + (1 * 210)] =
(0 + 2 + 0 + 8 + 16 + 0 + 0 + 128 + 256 + 512 + 1024) =
1946.

The following example shows addition in denary and binary number systems:

Denary Addition
3
+ 9
2 3 + 9 is greater than or equal to 10, so subtract 10 from 12 and write 2; carry the 1
1
3
+ 9
12 Bring the 1 carried over down to the tens column.
In this sample of denary addition, the number 12 is greater than or equal to its base (10), so we subtract 10 from 12 and write 2. We then carry the 10 over to the tens column and get the number 1210 (the number's base is written as a subscript to the right of the number, so the number 12 in base 10 is displayed 1210).

Binary Addition
1
+ 1
10
In this sample of binary addition, the number 2 is greater than or equal to its base (2), so we subtract 2 from 2 and write 0. We then carry the 10 over to the twos column and and get the number 102. Even though this may look like the number ten, it still has the value of 2; it looks like a ten because a binary number system has no way to represent the number two (remember it can only use zeros and ones). Now let's go back to our denary example (3 + 9) and see what that looks like in binary. In binary form, the number 3 is represented as 11 and the number 9 is represented as 1001:

Binary Addition Revisited 11
+ 1001
0 1 + 1 is greater than or equal to 2, so write 0 and carry 1...
1
11
+ 1001
00 1 + 1 is greater than or equal to 2, so write 0 and carry 1...
11
11
+ 1001
100 1 + 0 = 1
11
11
+ 1001
1100 0 + 1 = 1


Now we see that the denary number 1210 is equivalent to the binary number 11002.

Other Number Systems
The fun doesn't stop with binary numbers! One thing to keep in mind is that each base consists of all the integers that are less than the base. For example, base 2 includes 0-1, base 3 includes 0-2, base 8 includes 0-7, and so on.
As I said before, computers speak binary. A bit is a place in computer memory that can store one of two values, On or Off. However, as we saw with the number 194610, representing large numbers in binary quickly becomes unweildy. The solution is to group bits together into larger structures: nibbles are 4 bits, bytes are 8 bits, words are 16 bits, and double words are 32 bits. While a bit can only represent 2 values, a word (16 bits) can represent 216 values (216 = 65,536). The Hexadecimal number system (base 16) is convenient for dealing with computers because it helps to simplify binary numbers and converting between binary and hexadecimal is much easier than converting from binary to denary. Why is it easier? Because 16 has a natural relationship to 2 (16 = 24), while 10 does not easily translate to a power of 2 (10 = 23.32192809489...). I'll show an example a little later.

In order for humans to understand hexadecimal numbers, we have added the alphabetical characters A-F to the end of our number system. We can now count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, where A=10 and F=15. The calculator on this page uses the entire alphabet, so it can be used to calculate up to base 36. If you see alphabetical characters in the result set, do not be dismayed! The table at the bottom of this page translates base 36 numbers to our familiar denary system.

Ok, I promised to show how easy it is to convert from binary to hexadecimal. Let's go back to 194610, or 111100110102. The first step is to separate the binary number into groups of four:

0111 1001 1010 (Notice that I added a 0 to the left-hand side to make a complete set of four.)

Using the following table to translate each group of four, we get 79A16. While the 'A' in this number may look confusing at first, it is much easier to work with than 11110011010!

Binary Hexadecimal
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F


Base 36
symbol Base 10
Translation

0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
A 10
B 11
C 12
D 13
E 14
F 15
G 16
H 17
I 18
J 19
K 20
L 21
M 22
N 23
O 24
P 25
Q 26
R 27
S 28
T 29
U 30
V 31
W 32
X 33
Y 34
Z 35

Answer 2

there about 8 countries that use Denar .which one is first is a toss up.