What is the binary equivalent of the decimal number 368?a) 10111000 b) 110110000 c) 111010000 d) 111100000

Break Down the Problem

1. Identify the decimal number to convert: 368.
2. Convert the decimal number to binary.

Relevant Concepts

To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders. The binary equivalent is obtained by reading the remainders in reverse order.

Analysis and Detail

1. Divide 368 by 2:
   • 368 ÷ 2 = 184, remainder = 0
2. Divide 184 by 2:
   • 184 ÷ 2 = 92, remainder = 0
3. Divide 92 by 2:
   • 92 ÷ 2 = 46, remainder = 0
4. Divide 46 by 2:
   • 46 ÷ 2 = 23, remainder = 0
5. Divide 23 by 2:
   • 23 ÷ 2 = 11, remainder = 1
6. Divide 11 by 2:
   • 11 ÷ 2 = 5, remainder = 1
7. Divide 5 by 2:
   • 5 ÷ 2 = 2, remainder = 1
8. Divide 2 by 2:
   • 2 ÷ 2 = 1, remainder = 0
9. Divide 1 by 2:
   • 1 ÷ 2 = 0, remainder = 1

Now, write down the remainders from last to first:

$1 \, 0110 \, 1000$

Verify and Summarize

The binary representation of 368 is $101110000$ which corresponds to the second option in the provided choices.

Final Answer

The binary equivalent of the decimal number 368 is b) 110110000.