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All number systems are based on place values that are progressions of a base number raised to the 0, 1, 2, 3, 4... and so on. The base system we normally us is the decimal system or base ten system. In this system our place values are the

1's, 10's, 100's, 1000's, and so on.

Setting up a table from right to left it would look as follows:

1000's 100's 10's 1's place

3 2 1 o

10 10 10 10 base/exponent

For binary the base number would be 2 and the table would look like this:

32's 16's 8's 4's 2's 1's

5 4 3 2 1 o

2 2 2 2 2 2

Any number can be used as a base and organized in this manner. For example if you wanted to convert 27 to binary, you would go to the chart and subtract the largest availble number 16 from 27; place 1 in the 16's place, 1 in the 8's place, 0 in the 4's place (eight from eleven is 3)so you have 1 left in the 2's place and 1 in the 1's place or 11011. This makes sense if you think that this is from right to left is:

1 + 2 + 8 + 16 = 27

The same process can be used to convert any number to binary.

1. Go to the largest availble place and subtract.

2. See if you can repeat it with the remaining value in the next place if not put in a zero and continue this step until you can repeat step one.

31 in decimal = 11111

32 = 100000

33 = 100001

34 = 100010

35 = 100011

36 = 100100

37 = 100101

38 = 100110

39 = 100111

40 = 101000

Here are some other bases:

3's

27's 9's 3's 1's

4's

64's 16's 4's 1's

5's

125's 25's 5's 1's

16's (hexidecimal)

4096's 256's 16's 1's

Looking at this table you can get and idea why hexidecimal is used by computers. With each place capable of handling more numbers you can express larger numbers in less space.

Hexidecimal count

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

10 = 16

Take a look at 100.

decimal 100 = 64 hexidecimal (6 - 16's + 4 - 1's)

= 1100100 binary (64 + 32 + 4)

= 202 base7 (2 - 49's + 2 - 1's)

= 400 base5 (4 - 25's)

= 3201 base3 (3-27's + 2-9's + 1-1's)

The important thing to remember is that the pattern of all number systems is based on the base number raised to an exponent, and the first column is always the 1's.

1's, 10's, 100's, 1000's, and so on.

Setting up a table from right to left it would look as follows:

1000's 100's 10's 1's place

3 2 1 o

10 10 10 10 base/exponent

For binary the base number would be 2 and the table would look like this:

32's 16's 8's 4's 2's 1's

5 4 3 2 1 o

2 2 2 2 2 2

Any number can be used as a base and organized in this manner. For example if you wanted to convert 27 to binary, you would go to the chart and subtract the largest availble number 16 from 27; place 1 in the 16's place, 1 in the 8's place, 0 in the 4's place (eight from eleven is 3)so you have 1 left in the 2's place and 1 in the 1's place or 11011. This makes sense if you think that this is from right to left is:

1 + 2 + 8 + 16 = 27

The same process can be used to convert any number to binary.

1. Go to the largest availble place and subtract.

2. See if you can repeat it with the remaining value in the next place if not put in a zero and continue this step until you can repeat step one.

31 in decimal = 11111

32 = 100000

33 = 100001

34 = 100010

35 = 100011

36 = 100100

37 = 100101

38 = 100110

39 = 100111

40 = 101000

Here are some other bases:

3's

27's 9's 3's 1's

4's

64's 16's 4's 1's

5's

125's 25's 5's 1's

16's (hexidecimal)

4096's 256's 16's 1's

Looking at this table you can get and idea why hexidecimal is used by computers. With each place capable of handling more numbers you can express larger numbers in less space.

Hexidecimal count

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

10 = 16

Take a look at 100.

decimal 100 = 64 hexidecimal (6 - 16's + 4 - 1's)

= 1100100 binary (64 + 32 + 4)

= 202 base7 (2 - 49's + 2 - 1's)

= 400 base5 (4 - 25's)

= 3201 base3 (3-27's + 2-9's + 1-1's)

The important thing to remember is that the pattern of all number systems is based on the base number raised to an exponent, and the first column is always the 1's.