Question

21.509 base 10 to base 2

Answer 1

(21.508)₂ = ( ? )₂

=>(21.508)₁₀ is in decimal form we need to convert it into binary form.

=>First we need to convert the integral part of the decimal number to binary i.e.,21

=>dividing with 2 until quotient becomes zero will give us the binary value

1. 21/2 => remainder=1   quotient=10

2. 10/2 => remainder=0   quotient=5

3. 5/2    => remainder=1   quotient=2

4. 2/2    => remainder=0   quotient=1

5. 1/2    => remainder=1   quotient=0

=> binary format of 21 is (10101)₂. We got this by resultant remainders put in the obtained order.

=> Now find out the binary format of the decimal part i.e., 508

=> Multiplying with 2 and taking the integral part of resultant will be the binary part.

1. 0.508*2 = 1.016     integral part:1

2. 0.016*2 = 0.032     integral part:0

3. 0.032*2 = 0.064     integral part:0

resultant binary form:.(100)₂

=>Summing up integral and decimal parts together we get the following binary value.

      (10101.100)₂