Question

convert the given binary into decimal 1011.101​

Answer 1

 11.625 in decimal.

Explanation:

Thus 1011.101 in binary is equal to 11.625 in decimal.

Answer 2

The fractional binary number is converted into the floating point decimal number by using the two steps: One from integer part and other for fractional part.

Binary to decimal convergence:

Part 1:

• Convert the integer part of the binary number into the decimal number.

•  The integer part of the binary number 1011.101 is 1011. So on solving   it we get:

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

            1011= 8+0+2+1

            1011 = 11

• So, on converting 1011 binary number into its decimal equivalent we get 11.

Part 2:

• Convert the fractional part of the binary number into the decimal number.
• The fractional part of the binary number 1011.101 is 0.101. So on solving it we get:

           .101= $(1*1/2^1) + (0*1/2^2) + (1*1/2^3)$

           .101= $1*0.5 + 0*0.25 + 1*0.125$

           .101= 0.625

• So, on converting 0.101 binary number into its decimal equivalent we get 0.625.

• Lastly on adding the result of both the steps, the final answer can be achieved.

         1011.101​= 11+0.625

        1011.101= 11.625

So, the decimal equivalent of the binary number 1011.101 is 11.625.