Question

convert 564 from octal to decimal number system ​

Answer 1

Answer:

564 in binary

1011101002

Explanation:

In numeral system, we know octal is base-8 and binary is base-2. To convert octal 564 to binary, you follow these steps:

To do this, first convert octal into decimal, then the resulting decimal into binary

Start from one's place in octal : multiply ones place with 8^0, tens place with 8^1, hundreds place with 8^2 and so on from right to left

Add all the products we got from step 1 to get the decimal equivalent of given octal value.

Then, divide decimal value we got from step-2 by 2 keeping notice of the quotient and the remainder.

Continue dividing the quotient by 2 until you get a quotient of zero.

Then just write out the remainders in the reverse order to get binary equivalent of decimal number.

First, convert 564₈ into decimal, by using above steps:

= 564₈

= 5 × 8²+ 6 × 8¹ +4 × 8⁰

= 372₁₀

Now, we have to convert 372₁₀ to binary

372 / 2 = 186 with remainder 0

186 / 2 = 93 with remainder 0

93 / 2 = 46 with remainder 1

46 / 2 = 23 with remainder 0

23 / 2 = 11 with remainder 1

11 / 2 = 5 with remainder 1

5 / 2 = 2 with remainder 1

2 / 2 = 1 with remainder 0

1 / 2 = 0 with remainder 1

Then just write down the remainders in the reverse order to get the answer, The octal number 564 converted to binary is therefore equal to :

101110100