Question

convert the following binary numbers into decimal numbers a).1111.11​

Answer 1

Answer:

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Explanation:

1111.11 from binary to decimal is 15.75.

Answer 2

To convert binary number 1111.11, we convert its integral and fractional part individually and then add them to get the equivalent decimal number, as below:

In integral part of binary number, multiply ones place with 2^0, tens place with 2^1, hundreds place with 2^2 and so on from right to left.

In the fractional part of binary number, multiply tenths place by 2^-1, hundredths place by 2^-2 and so on from left to right

Add them all together you got from step 1 & step 2 to get decimal equivalent of 1111.11.

Using the above steps, we first convert the integral part 1111 to decimal number (Don't forget that we start from ones place to so on...)

Decimal equivalent of "1" = 1 × 2^0 = 1

Decimal equivalent of "1" = 1 × 2^1 = 2

Decimal equivalent of "1" = 1 × 2^2 = 4

Decimal equivalent of "1" = 1 × 2^3 = 8

Decimal equivalent of "1111" = 8421

1111 = 15

Now we will convert the fractional part 0.11 to decimal form (Don't forget that we start from tenths palce to so on..):

Decimal equivalent of "1" = 1 × 2^-1 = 0.5

Decimal equivalent of "1" = 1 × 2^-2 = 0.25

Decimal equivalent of "0.11" = 0.50.25

0.11 = 0.75

Here is the final answer, The binary number 1111.11 converted to decimal is therefore equal to:

= 1111.112

= 1510 + 0.7510

= 15.7510