Question

The decimal equivalent of the binary number (1011.011)2 is

Answer 1

Answer:

11.375

Explanation:

1011.011 from binary to decimal is 11.375.

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Answer 2

After converting the binary number '1011.011' into the decimal number, final answer obtained is '11.375'.

Binary to Decimal conversion:

Firstly, the integer part of the given binary number is solved by following the given set of operations.

• From left to right direction keep on multiplying each digit separately by $2^0, 2^1, 2^3, 2^4$…. respectively.

• After completing the step one, add on all the numbers.

• So after converting the integer part of the given binary number it will become:

                    1011 =     $1*2^3 + 0* 2^2+ 1*2^1+ 1 * 2^0$

•             1011 = 8+0+2+1
•          
•   1011 = 11

Then, comes the fractional part of the binary number.

• Staring in right to left direction divide each digit by $2^1, 2^2, 2^3, 2^4$... respectively.
• After completing the step one, add on all the numbers.
• So after converting the decimal part of the given binary number it will become:

            0.011 =  $(0*1/2) + (1*1/2^2) + (1*1/2^3)$

            0.011  = 0.375

Then, for achieving the final answer, performed addition on both the numbers generated from solving integer and fractional part of the binary number.

So the decimal equivalent of the binary number is : 11+0.375 = 11.375

After adding the numbers that obtained in the above steps we get the decimal representation of the given binary number.