Sunday 7 September 2014

Number System Conversion - Binary to any base (Radix) conversion:

NUMBER SYSTEMS CONVERSION:

Binary to any base (Radix) conversion:

1.      Binary to decimal number conversion
2.      Binary to Octal number conversion
3.      Binary to Hexadecimal number conversion

Octal to any base (Radix) conversion:

1.      Octal to decimal number conversion
2.      Octal to binary number conversion
3.      Octal to Hexadecimal number conversion

Decimal to any base (Radix) conversion:

1.      Decimal to binary number conversion
2.      Decimal to Octal number conversion
3.      Decimal to Hexadecimal conversion

Hexa decimal to any base (Radix) conversion:

                       1.   Hexadecimal to binary number conversion
                       2.      Hexadecimal to Octal number conversion
                       3.      Hexadecimal to decimal number conversion


 Binary to any base (Radix) conversion:

1.      Binary to decimal number conversion                 * * * * * * * * * * * * * * * * * * * * *

Ex(1): Convert  (11111)2 to decimal
Sol:  The equivalent decimal number is
                  = 1x24 + 1x23 + 1x22 + 1x21 + 1x20
                  = 16+8+4+2+1             = (31)10
Ex(2): Convert decimal equivalent of the number 10101
Sol:  The equivalent decimal number is
=  1x24 + 0x23 + 1x22 + 0x21 + 1x20
                  = 16+4+1
                  = (21)10
Ex(3): Find the decimal equivalent of the binary number (110101)
Sol:  The equivalent decimal number is
                  = 1x25 +1x24 + 0x23 + 1x22 + 0x21 + 1x20
                                    =32+16+4+1
                  = (53)10
Ex(4):  Convert (101101)2 to decimal
Sol:   The equivalent decimal number is
                  =1x25 + 0x24 + 1x23 + 1x22 + 0x21 + 1x20
                                    =32+8+4+1  = (45)10
Ex(5): Determine the decimal number of the following binary number
             (101101.10101)
Sol:      The equivalent Decimal number is
             = 1x25+0x24+1x23+1x22+0x21+1x20. 1x2-1+0x2-2+1x2-3+0x2-4+1x2-5
             = 32 + 8 +4 +1 + (1/2) + (1/8) + (1/32)
             = (45.65625)10
 Ex(6): Convert decimal equivalent of the number (0.1011)
         Sol:      The equivalent Decimal number is
                    = 1x2-1+0x2-2+1x2-3+1x2-3+1x2-4
                    = (1/2) + 0 + (1/8) + (1/16)
                    = (0.6875)10                  
      Ex (7): convert 1101110.011 to decimal
       Sol: 
                =1x26  + 1x25  + 0x24 + 1x23 + 1x22 + 1x21 +0x20 .0x2-1 + 1x2-2 + 1x2-3
                = 64+32+0+8+4+2+0.0+1/4+1/8
                = (110.375)10
       Ex (8): (1001.0101)2  to decimal form
       Sol:  
                       = 1x23 + 0x22  + 0x21 + 1x20 .0x2-1 + 1x2-2 + 0x2-3 + 0x2-4
                      =    8+0+0+1.0+1/4+0+1/16
              = (9.3125)10
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