BINARY TO DECIMAL CONVERSION

May 6 • General • 2747 Views • 2 Comments on BINARY TO DECIMAL CONVERSION

BINARY TO DECIMAL CONVERSION

  • DECIMAL NUMBER SYSTEM

The Decimal number system has a base of 10 ,and is a position value system .The statement ‘the decimal number system has a base of 10’ implies that it contains ten unique symbols(or digits) i.e 0,1,2,3,4,5,6,7,8 and 9.The ten digits do not limit us to express only ten different quantites because we use the various digits in appropriate positions within a number to indicate the magnitude of the quantity.For expressing quantities exeeding nine,two or more digits are used,and the position of each digit within the number indicates the magnitude it represents.The placement of the digits in the sequenced order from right  to left is understood to carry a specific meaning.

  • BINARY NUMBER SYSTEM

The  binary number system is simply another way to count.It is less complicated than the decimal number system because it is composed of only two digits 0 and 1.Just as the Decimal number system with its ten digits is a base 10 system,the binary system with its two digits is a base 2 system.These two digits namely 0 and 1 carry the same meaning as in the decimal system but different meaning is given to the position occupied by the numeral or digit. In a binary system ,the base is 2 ,so any number can be expressed by an array of numerals representing the cofficients of power of 2 and not 10.In a binary system,the weight of each successively higher posotion (to the left) is an increasing power of 2.

Table showing binary number of decimal number

Decimal numberEqivalent Binary number
00000
10001
20010
30011
40100
50101
60110
70111
81000
91001
101010
111011
121100
131101
141110
151111

 

BINARY-TO-DECIMAL CONVERSION

The binary number system is a positional system where each binary digits (bit) carries a certain weight based on its position relative to the least significant bit (LSB). The right-most bit is the LSB  in a binary number and has a weight of  2˄0=1 .Any number can be converted to its  decimal equivalent simply by adding the products of each bit and its weight.

For Example

10011=1(2˄4)+0(2˄3)+0(2˄2)+ 1(2˄1)+1(2˄0)                 

           =16+0+0+2+1

            =19

Fraction number can be represented in binary by placing bits to the right of the binary point ,just as fractional digits are placed to the right of the decimal point.The column weight of a binary number are:

2˄n….   2˄2   2˄1    2˄0   .  2˄-1   2˄-2….2˄-n

For Example

 0.1001=1(2˄-1)+0(2˄-2)+0(2˄-3)+ 1(2˄-4)   

             =1*0.5+0*0.25+0*0.125+1*0.0625

             =0.5625    

QUESTION WITH ANSWER

Q:Convert (110110)2     to its Decimal equivalent?

Ans:binary weight :2˄5   2˄4   2˄3    2˄2   2˄1   2˄0

        Weight value:  32      16      8        4         2      1

        Binary number:1        1        0        1         1      0

So, (110110)2    = 1*32+1*16+8*0+1*4+2*1+1*0

                         =(54)10

Q:Convert the binary fractional number 0.1101 into its Decimal equivalent?

Ans:binary weight :2˄-1      2˄-2         2˄-3         2˄-4 

        Weight value:  0.5       0.25         0.125        0.0625  

        Binary number:1           1                  0             1        

So, (110110)2    = 1*0.5+1*0.25+0*0.125+1*0.0625

                         =(0.8125)10

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2 Responses to BINARY TO DECIMAL CONVERSION

  1. Sounak Ghosh says:

    The binary to decimal conversion is an essential aspect in digital electronic circuits and computer applications as well.This article shows the basic and easiest conversion methods along with apropriate examples..

  2. Ritika Savita says:

    The Binary-Decimal Conversion system is the most basic conversion system, among others. It forms the basic logic of appkication in many electronic devices, which work on binary system. Infact, complete electronics is based on the binary mathematics.

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