Question

convert the following binary numbers into decimal number 11001.101 please answer step by step​

Answer 1

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1. the the last three digits -101 after the . will give us 2

2. now 11001 shall be converted.

3. From right to left: 1+0+0+8+16=25

4. hence , the decimal conversion of 11001.101 in decimal is 25.2

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Answer 2

To convert binary number 11001.101, 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 11001.101.

Using the above steps, we first convert the integral part 11001 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 "0" = 0 × 2^1 = 0
Decimal equivalent of "0" = 0 × 2^2 = 0
Decimal equivalent of "1" = 1 × 2^3 = 8
Decimal equivalent of "1" = 1 × 2^4 = 16
Decimal equivalent of "11001" = 168001
11001 = 25

Now we will convert the fractional part 0.101 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 "0" = 0 × 2^-2 = 0
Decimal equivalent of "1" = 1 × 2^-3 = 0.125
Decimal equivalent of "0.101" = 0.500.125
0.101 = 0.625

Here is the final answer, The binary number 11001.101 converted to decimal is therefore equal to:
= 11001.1012
= 2510 + 0.62510
= 25.62510