Conversion of Binary to Decimal:

In the case of Integer numbers, to convert a binary number to a decimal number, the whole digit of the binary must be multiplied by the local value (2^{x}, 2 is the base of binary). In the case of fractions, the digits have to multiply their local value (2^{x}). Here you have to set values like x = -1, -2, -3 from MSB to LSB.

MSB = Most Significant bit

LSB = Least Significant Bit.

Note: x^{0} = 1 and x^{1} = x | Here ‘x’ is any number.

Here,

If x = 1, 2, 3 ————.

For example, if x = 1 then 2^{-1} = 1/2

If x = 2 then 2^{-2} =1/4

If x = 3 then 2^{-3} = 1/8———- etc.

**Example 1:
**

(11011. 101)

_{2 }, to determine the value of the equivalent decimal number:

(11011.101)

_{2}= 1 × 2

^{4}+ 1 × 2

^{3}+ 0 x 2

^{2}+ 1+ 2

^{1}+ 1 x 2

^{0}+1 x 2

^{-1 }+ 0 x 2

^{-2}+ 1 x 2

^{-3}

= 16 + 8 + 0 + 2 + 1 + 1/2 + 0 +1/8

= 27 + 0.5 + 0.125

= (27.625)_{10}

So (11011.101)_{2} = (27.625)_{10} **(Answer)
**

**Example 2:**

(1100011.011)

_{2, }to determine the value of the equivalent decimal number: (1100011.011)

_{2}= 1 x 2

^{6}+ 1 x 2

^{5}+ 0 x 2

^{4}+ 0 x 2

^{3}+ 0 x 2

^{2}+ 1 + 2

^{1}+ 1 x 2

^{0}+ 0 x 2

^{-1}+ 1 x 2

^{-2}+ 1 x 2

^{-3}

= 64 + 32 + 0 + 0 + 0 + 2 + 1 + 0 +1/4+1/8

= 99 + 0.25 + 0.125

= 99.375

= (1100011.011)

_{2}= (99.375)

_{10}

**(Answer)**