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BINARY NUMBER SYSTEM

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NUMBER SYSTEM
DECIMAL NUMBER SYSTEM
BINARY NUMBER SYSTEM
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HEXADECIMAL NUMBER SYSTEM

 Binary Number System

            - The binary number system (base 2) uses only 0s and 1s. Its a place value system with the following values for its 8 positive columns.

    27         26            25            24            23            22            21            20

dec. value         128         64             32             16           8              4               2              1

        Every position is a bit, either 0 or a 1. An 8-bit number is a byte inside the computer. The range of possible positive values that one byte can represent is 0 to 225. The maximum, 225, will occur when all 8 bits are 0s.

Converting Binary to Decimal

 111Ø12

            =1x24 + 1x23 + 1x22 + 0x21 + 1x2o

            = 8 + 4 + 2 + 0

            = 1410

 111ØØ2

            =1x24 + 1x23 + 1x22 + 0x21 + 0x20

            =16 + 8 + 4 + 0

            =2810

 1Ø11112

            =1x25 + 0x24 + 1x23 + 1x22 + 1x21 + 1x20

            =32 + 0 + 8 + 4 + 2 + 1

            =4710

 1ØØØ112

            =1x25 + 0x24 + 0x23 + 0x22 + 1x21 + 1x20

            =32 + 2 + 1

            =3510

1Ø1Ø12

            =1x24 + 0x23 + 1x22 + 0x21 + 1x20

            =16 + 4 + 1

         =2110