TUTORIALS

DOS Quiz
DOS Exam

## Binary

Computers work on the principle of number manipulation. Inside the computer, the numbers are represented in bits and bytes. For example, the number three is represented by a byte with bits 0 and 1 set; 00000011. This is numbering system using base 2. People commonly use a decimal or Base 10 numbering system. What this means is that in Base 10, count from 0 to 9 before adding another digit. The number 22 in Base 10 means we have 2 sets of 10's and 2 sets of 1's.

Base 2 is also known as binary since there can only be two values for a specific digit; either a 0 = OFF or a 1 = ON. You cannot have a number represented as 22 in binary notation. The decimal number 22 is represented in binary as 00010110 which by following the below chart breaks down to:

 Bit Position 7 6 5 4 3 2 1 0 1 1 1 1 1 1 1 1 Decimal 128 64 32 16 8 4 2 1

22 or 00010110:

All numbers representing 0 are not counted, 128, 64, 32, 8, 1 because 0 represents OFF

However, numbers representing 1 are counted, 16 + 4 + 2 = 22 because 1 represents ON

Decimal Values and Binary Equivalents chart

 Decimal Binary 1 1 2 10 3 11 4 100 5 101 6 110 7 111 8 1000 9 1001 10 1010 16 10000 32 100000 64 1000000 100 1100100 256 100000000 512 1000000000 1000 1111101000 1024 10000000000

The other major numbering system used by computers is hexadecimal, or Base 16. In this system, the numbers are counted from 0 to 9, then letters A to F before adding another digit. The letter A through F represent decimal numbers 10 through 15, respectively. The below chart indicates the values of the hexadecimal position compared to 16 raised to a power and decimal values. It is much easier to work with large numbers using hexadecimal values than decimal.

To convert a value from hexadecimal to binary, you merely translate each hexadecimal digit into its 4-bit binary equivalent. Hexadecimal numbers have either and 0x prefix or an h suffix. For example, the hexadecimal number:

0x3F7A

Translates into, Using the Binary chart and the below chart for Hex:

0011 1111 0111 1010

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