$(630)_{10} = (\space\space\space\space)_2
Answer (2)
Divide the decimal number 630 repeatedly by 2, noting the remainders at each step.
The remainders are: 0, 1, 1, 0, 1, 1, 1, 0, 0, 1.
Read the remainders in reverse order to obtain the binary representation: 1001110110.
Therefore, the binary representation of 630 is 1001110110 .
Explanation
Understanding the Problem We need to convert the decimal number 630 to its binary equivalent. This means we want to express 630 as a sum of powers of 2.
Method We will repeatedly divide 630 by 2 and record the remainders. The remainders, when read in reverse order, will give us the binary representation.
Repeated Division
Divide 630 by 2: 630 ÷ 2 = 315 with a remainder of 0.
Divide 315 by 2: 315 ÷ 2 = 157 with a remainder of 1.
Divide 157 by 2: 157 ÷ 2 = 78 with a remainder of 1.
Divide 78 by 2: 78 ÷ 2 = 39 with a remainder of 0.
Divide 39 by 2: 39 ÷ 2 = 19 with a remainder of 1.
Divide 19 by 2: 19 ÷ 2 = 9 with a remainder of 1.
Divide 9 by 2: 9 ÷ 2 = 4 with a remainder of 1.
Divide 4 by 2: 4 ÷ 2 = 2 with a remainder of 0.
Divide 2 by 2: 2 ÷ 2 = 1 with a remainder of 0.
Divide 1 by 2: 1 ÷ 2 = 0 with a remainder of 1.
Binary Representation Now, we read the remainders in reverse order: 1001110110. This is the binary representation of 630.
Final Answer Therefore, ( 630 ) 10 = ( 1001110110 ) 2 .
Examples
Binary numbers are the language of computers. Every piece of data, from text to images to videos, is stored as a sequence of 0s and 1s. Converting decimal numbers to binary is essential in computer science for understanding how computers store and process information. For example, if you want to understand how much memory a file takes up on your computer, you need to understand binary representation.
To convert 630 from decimal to binary, we repeatedly divide by 2, noting the remainders. The remainders, read in reverse order, give us the binary representation: 1001110110 . Thus, ( 630 ) 10 = ( 1001110110 ) 2 .
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