How can I convert between binary/hexadecimal numbers with decimals into a decimal number system

Question

I was wondering on how to convert between number systems when the factor of decimal in binary and hexadecimal numbers is in play. For example,

Convert 011010.011b into a decimal number system

or

Convert 1C0DE.4Ah into a decimal number system

Answer 1

 

I have written the procedure down, please click the link

https://imgur.com/gallery/2N4eqBb

And you can also click the links of WolframAlpha below to check the answers

011010.011 in binary to decimal

1C0DE.4A base16 to decimal

Comments

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Answer 2

The process of converting binary or hexadecimal (with fractions) to decimal is the same.

An example with binary (I'll be using 1101.001b for my example instead of 011010.011b):

Step 1) Convert the left side of the binary number to decimal:

$1101 = (1 * 2^{^{3}}) + (1 * 2^{^{2}}) + (0 * 2^{^{1}}) + (1 * 2^{^{0}}) = 13$

Step 2) The process for converting the right side of the binary number is similiar, but instead of multiplying each individual binary digit by $2^{^{n}}$, you'll be multiplying by $1/2^{^{n}}$. Note however that unlike the conversion above, you do not start with a power of 0, but instead you start with a power of 1, and the power increases the further to the right you move in decimal places.

$.001 = (0 * 1/2^{^{1}}) + (0 * 1/2^{^{2}}) + (1 * 1/2^{^{3}}) = 0.125$

Step 3) Add the left side and right side back together

13 + 0.125 = 13.125

Answer 3

Hey!

 for example lets take the first part:

(011010.011 b to decimal)

integer part(011010)

(0 * 2⁰ ) + (1 * 2¹) + (0 * 2² )+(1 * 2³ )+ (1* 2⁴) +(0* 2⁵) = 26

now the decimal part:( 011)

(1* 2⁰) + (1* 2¹) + (0* 2²)= 3

 hence the approximate ans is 26.3

 And when we check for the same in WolfFramAlpha  the answer is 26.375 

 

Similarly the second part:

(1C0DE.4A h to decimal)

integer part:(1CODE)

( E* 16⁰)+ (D* 16¹)+(0* 16²)+ (C*16³)+(1*16⁴)    { E=14  D=13  C=12  A=10)

= 114910

Decimal part :(4A)

(A*16⁰) +( 4* 16¹)= 74

Hence ans is 114910.74

and on WolfFramAlpha it shows 114910.2890625