To convert each of the decimal numbers (256, 1324, 11011, and 456) to their binary form, we follow these steps:

1. Decimal to Binary Conversion:

256 in Binary:

• Divide 256 by 2:
  • 256 ÷ 2 = 128 remainder 0
  • 128 ÷ 2 = 64 remainder 0
  • 64 ÷ 2 = 32 remainder 0
  • 32 ÷ 2 = 16 remainder 0
  • 16 ÷ 2 = 8 remainder 0
  • 8 ÷ 2 = 4 remainder 0
  • 4 ÷ 2 = 2 remainder 0
  • 2 ÷ 2 = 1 remainder 0
  • 1 ÷ 2 = 0 remainder 1

Therefore, $256_{10} = 100000000_2$

1324 in Binary:

• Divide 1324 by 2:
  • 1324 ÷ 2 = 662 remainder 0
  • 662 ÷ 2 = 331 remainder 0
  • 331 ÷ 2 = 165 remainder 1
  • 165 ÷ 2 = 82 remainder 1
  • 82 ÷ 2 = 41 remainder 0
  • 41 ÷ 2 = 20 remainder 1
  • 20 ÷ 2 = 10 remainder 0
  • 10 ÷ 2 = 5 remainder 0
  • 5 ÷ 2 = 2 remainder 1
  • 2 ÷ 2 = 1 remainder 0
  • 1 ÷ 2 = 0 remainder 1

Therefore, $1324_{10} = 10100101100_2$

11011 in Binary:

• Divide 11011 by 2:
  • 11011 ÷ 2 = 5505 remainder 1
  • 5505 ÷ 2 = 2752 remainder 1
  • 2752 ÷ 2 = 1376 remainder 0
  • 1376 ÷ 2 = 688 remainder 0
  • 688 ÷ 2 = 344 remainder 0
  • 344 ÷ 2 = 172 remainder 0
  • 172 ÷ 2 = 86 remainder 0
  • 86 ÷ 2 = 43 remainder 0
  • 43 ÷ 2 = 21 remainder 1
  • 21 ÷ 2 = 10 remainder 1
  • 10 ÷ 2 = 5 remainder 0
  • 5 ÷ 2 = 2 remainder 1
  • 2 ÷ 2 = 1 remainder 0
  • 1 ÷ 2 = 0 remainder 1

Therefore, $11011_{10} = 10101111100011_2$

456 in Binary:

• Divide 456 by 2:
  • 456 ÷ 2 = 228 remainder 0
  • 228 ÷ 2 = 114 remainder 0
  • 114 ÷ 2 = 57 remainder 0
  • 57 ÷ 2 = 28 remainder 1
  • 28 ÷ 2 = 14 remainder 0
  • 14 ÷ 2 = 7 remainder 0
  • 7 ÷ 2 = 3 remainder 1
  • 3 ÷ 2 = 1 remainder 1
  • 1 ÷ 2 = 0 remainder 1

Therefore, $456_{10} = 111001000_2$

Summary:

• 256 in binary: $100000000_2$
• 1324 in binary: $10100101100_2$
• 11011 in binary: $10101111100011_2$
• 456 in binary: $111001000_2$

Verification:

You can verify these conversions by converting the binary numbers back to decimal:

• $100000000_2 = 256$
• $10100101100_2 = 1324$
• $10101111100011_2 = 11011$
• $111001000_2 = 456$

Each conversion is correct.

Would you like more details or have any questions?

Related Questions:

1. How do you convert larger decimal numbers to binary efficiently?
2. What is the method for converting binary back to decimal?
3. How does the binary system relate to the hexadecimal system?
4. What is the use of binary numbers in computer systems?
5. Can negative decimal numbers be represented in binary?

Tip:

When converting large numbers to binary, breaking the process into steps and organizing the remainders can make it easier to track your work!