convert 4867 to binary

Question

I want help with convert 4867 to binary

 

thanks

Answer 1

Like decimal, binary is a positional number system.  Going from right to left, each bit (binary digit) is the remainder after dividing by 2 repeatedly (that is, powers of 2).

 

So, to convert 13 to binary:

   divide 13 by 2 and get a quotient of 6 and a remainder of 1

   divide 6 by 2 and get 3 with a remainder of 0

   divide 3 by 2 and get 1 with a remainder of 1

   divide 1 by 2 and get 0 with a remainder of 1

Reading the remainders in l-to-r order (bottom to top), 13 (decimal) is 1101 (binary).

 

Note: to convert from decimal to either octal or hexadecimal is pretty easy (if you have practice), then converting to binary is easy (see Kenneth S's post).

 

convert 4867 to binary

Divide 4867 by 2 and get 2433 with a remainder of 1

Divide 2433 by 2 and get 1216 with a remainder of 1

Divide 1216 by 2 and get 608 with a remainder of 0

Divide 608 by 2 and get 304 with a remainder of 0

Divide 304 by 2 and get 152 with  remainder of 0

Divide 152 by 2 and get 76 with a remainder of 0

Divide 76 by 2 and get 38 with a remainder of 0

Divide 38 by 2 and get 19 with a remainder of 0

Divide 19 by 2 and get 9 with a remainder of 1

Divide 9 by 2 and get 4 with a remainder of 1

Divide 4 by 2 and get 2 with a remainder of 0

Divide 2 by 2 and get 1 with a remainder of 0

Divide 1 by 2 and get 0 with a remainder of 1     [note: don't stop too early]

 

The result:

    1 0011 0000 0011  

[write as hexadecimal groups of 4 bits much like we use commas to separate large decimal numbers]

Answer 2

the best way, in my experience, is to convert to OCTAL.  from that result, you can write each octal digit (0 thru 7) in the form of 3 bits, then group this bit string into groups of 4 bits, working from right to left, and read them as 0 thru F, which are the sixteen hexadecimal digit names.

 

Here's an example: convert 941 to octal; all the process below uses decimal numbers

a) division by 8 gives REMAINDER 5 and quotient 117

b) division by of 117 by 8 gives remainder 5, again, and quotient 14

c) division of 14 by 8 gives remainder 6 and quotient 1...since quotient < 8, the process is done and the OCTAL representation of the original decimal 941 is 1655, consisting of base 8 digits that are assembled in order from right to left according to the remainders that we developed (& ending with the last quotient < 8)

 

Now, just read out these in binary, from left to right:  1 110 101 101 and then group them 4 at a time (working R to L) and you have 3AD.

 

Check your work: 3(16²) + 10(16) + 13 = 941.