Convert this decimal number to its binary, octal and hexadecimal representations:
248
binary:
octal:
hexadecimal:

Explanation:

In binary the numbers are represented with 0 or 1

Make a table using numbers written in powers of two, like this:

2^n        2^(n-1)    ...     2^1       2^0

1 OR 0   1 OR 0   ...     1 OR 0  1 OR 0

1 or 0 represents the binary digit of the number up in the column, so adding numbers from left to right and then taking their respecting binary representation will deliver to the binary representation. n is the max. number until 2^n > Number in decimal

In this example:

2^7  2^6  2^5   2^4   2^3  2^2  2^1  2^0

128   64  32  16  8  4  2  1

1   1  1  1  1  0  0  0

Making the sum: 128 + 64 + 32 + 16 + 8 = 248

So the binary representation of 248 is (11111000)₈

In octal the numbers are represented with combinations of 0 to 8

Start by dividing 248 by 8:

248÷8 = 31 ⇒ Take the Remainder ( in this case is 0) and insert it like this:

_ _ 0  where the blank spaces will be filled with the Remainder of the divisions.

Then, take 31 and divide it by 8:

31÷8= 3 ⇒ Take the remainder that is 7 and insert it in the created field (previously we have inserted 0):

_ 7 0

Repeat this method:

3÷8=0 ⇒ Remainder = 3

The final field is :  3 7 0

So the octal representation of 248 is (370)₈

In hexadecimal representations the numbers are represented with combinations of symbols:  0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F; Where :

Start like the octal form, just dividing by 16:

First, 248÷16= 15⇒ Remainder 8, take the remainder 8 and put it on a field like before:

_ 8

Then, 15÷16=0 ⇒ Remainder 15, take the remainder 16 and put it on the field, but remember (15)₁₀=F₁₆

F 8

Finally  the field is F8

So the Hexadecimal representation of 248 is (F8)₁₆

no

explanation

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