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Binary to Decimal Conversion


Binary to Decimal Conversion

The decimal equivalent of a binary number is obtained by multiplying each binary digit with its positional value.

The Definition of the Positional Value

The right most bit has positional value 20 or 1 the second right most bit has value 21 or 2 and so one.

Comparison with the Decimal System.

To better undestand the analogy with the decimal system. Consider this – the right most bit has positional value 100 or 1 the second right most bit has value 101 or 10,  the  third right most bit has value 102 or 100 and so one.

Example 1

Convert the binary number 11001 into its decimal equivalent.

Answer

11010 (Binary number) =1×24 +1×23 +0x22 +1×21+0x20=16+8+0+2+0=26(Decimal Number)

(11001)2 =(26)10

Example 2
Convert 111101101112 to decimal equivalent number,

Answer

111101101112 =1×210 +1×29+1×28 +1×27+0x26+1×25+1×24+0x23+1×22+1×21+1×20=197510

To under stand it with existing Decimal system consider expression of th value of the 345 in decimal system with base 10. It can be expressed as

345 = 3×102 +4×101+5×100

 

 

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