The last three digits in the binary representation of `(365247728)_(10)` is :

Options

A. `000`
B. `100`
C. `110`
D. `010`

Answer

To find the last three digits in the binary representation of the decimal number \( (365247728)_{10} \), we can follow these steps:

### Step 1: Convert the Decimal Number to Binary
To convert a decimal number to binary, we can repeatedly divide the number by 2 and keep track of the remainders. The binary representation is formed by the remainders read in reverse order.

### Step 2: Perform the Division
Let's divide \( 365247728 \) by \( 2 \) and keep track of the remainders:

1. \( 365247728 \div 2 = 182623864 \) remainder \( 0 \)
2. \( 182623864 \div 2 = 91311932 \) remainder \( 0 \)
3. \( 91311932 \div 2 = 45655966 \) remainder \( 0 \)
4. \( 45655966 \div 2 = 22827983 \) remainder \( 0 \)
5. \( 22827983 \div 2 = 11413991 \) remainder \( 1 \)
6. \( 11413991 \div 2 = 5706995 \) remainder \( 1 \)
7. \( 5706995 \div 2 = 2853497 \) remainder \( 1 \)
8. \( 2853497 \div 2 = 1426748 \) remainder \( 1 \)
9. \( 1426748 \div 2 = 713374 \) remainder \( 0 \)
10. \( 713374 \div 2 = 356687 \) remainder \( 0 \)
11. \( 356687 \div 2 = 178343 \) remainder \( 1 \)
12. \( 178343 \div 2 = 89171 \) remainder \( 1 \)
13. \( 89171 \div 2 = 44585 \) remainder \( 1 \)
14. \( 44585 \div 2 = 22292 \) remainder \( 1 \)
15. \( 22292 \div 2 = 11146 \) remainder \( 0 \)
16. \( 11146 \div 2 = 5573 \) remainder \( 0 \)
17. \( 5573 \div 2 = 2786 \) remainder \( 1 \)
18. \( 2786 \div 2 = 1393 \) remainder \( 0 \)
19. \( 1393 \div 2 = 696 \) remainder \( 1 \)
20. \( 696 \div 2 = 348 \) remainder \( 0 \)
21. \( 348 \div 2 = 174 \) remainder \( 0 \)
22. \( 174 \div 2 = 87 \) remainder \( 0 \)
23. \( 87 \div 2 = 43 \) remainder \( 1 \)
24. \( 43 \div 2 = 21 \) remainder \( 1 \)
25. \( 21 \div 2 = 10 \) remainder \( 1 \)
26. \( 10 \div 2 = 5 \) remainder \( 0 \)
27. \( 5 \div 2 = 2 \) remainder \( 1 \)
28. \( 2 \div 2 = 1 \) remainder \( 0 \)
29. \( 1 \div 2 = 0 \) remainder \( 1 \)

### Step 3: Collect the Remainders
Now, we collect the remainders from the last division to the first:
- Reading from bottom to top, the binary representation of \( 365247728 \) is \( 101011111110011111110000000 \).

### Step 4: Identify the Last Three Digits
The last three digits of the binary representation \( 101011111110011111110000000 \) are \( 000 \).

### Final Answer
Thus, the last three digits in the binary representation of \( (365247728)_{10} \) are \( 000 \).

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