The Decimal & Binary System and Converting between Binary and Decimal

I am assuming that a basic knowledge of binary and decimal notation is known, if you are unfamiliar with it, read up on binary and decimal

The decimal system has a base or radix of 10 – this means that each digit in the number is multiplied by 10 raised to a power corresponding to that digits position.

The same principles holds for decimal fractions but negative powers of 10 are used

A number with both an integer and fractional part has digits raised to both positive and negative powers of 10

In the binary system we have only two digits, 1 & 0 to represent numbers

To convert from binary to decimal, all that is required is to multiply each binary digit by the appropriate power of 2 and add the results

To convert from decimal to binary, the integer and fractional parts are handled separately

Hexadecimal Notation

Because of the inherent binary nature of digital computer components, all forms of data within computers are represented by various binary codes, however the binary system is cumbersome for human beings, thus we use a more compact notation called hexadecimal.

Binary digits are grouped into sets of four, each possible combination of four binary digits is given a symbol as follows

0000 = 0

0100 = 4

1000 = 8

1100 = C

0001 = 1

0101 = 5

1001 = 9

1101 = D

0010 = 2

0110 = 6

1010 = A

1110 = E

0011 = 3

0111 = 7

1011 = B

1111 = F

A sequence of hexadecimal digits can be thought of as representing an integer in base 16, thus 2C = (2H * 16^1) + (CH * 16^0) = (2 * 16^1) + (12 x 16^0) = 44

Hexadecimal notation is used not only to represent integers, it is also used as a concise notation for representing any sequence of binary digits

Decimal

Binary

Hex

0

0000

0

5

0011

5

15

1111

F

16

0001 0000

10

31

0001 0000

1F

255

1111 0000

FF

256

0001 0000 0000

100

Benefits of using hexadecimal include

It is more compact than binary notation

In most computers, binary data occupy some multiple of 4 bits, and hence some multiple of a single hexadecimal digit

It is extremely easy to convert between binary and hexadecimal

Posted on Monday, January 30, 2012 6:35 AM | Back to top

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