The binary equivalent of the decimal number 8 is __________.

The correct answer is 1000.

Key Points

• The binary number system is a base-2 numeral system that uses only two digits: 0 and 1.
• To convert a decimal number (base-10) to binary (base-2), divide the number by 2 and record the remainders until the quotient becomes 0.
• The decimal number 8 can be converted to binary using repeated division: 8 ÷ 2 = 4 remainder 0, 4 ÷ 2 = 2 remainder 0, 2 ÷ 2 = 1 remainder 0, 1 ÷ 2 = 0 remainder 1.
• Reading the remainders from bottom to top gives the binary equivalent of 8: 1000.
• Binary numbers are widely used in computer systems and digital electronics for data representation and processing.

Additional Information

• Binary Number System:
  • The binary numeral system represents numbers using only two symbols: 0 and 1.
  • It is the foundation of computer systems, where each binary digit (bit) represents a unit of data.
• Decimal to Binary Conversion:
  • Divide the decimal number by 2 and note the remainder.
  • Repeat the process until the quotient becomes 0.
  • Read the remainders in reverse order (bottom to top) to form the binary number.
• Applications of Binary Numbers:
  • Used in computer architecture, programming, and data storage.
  • Binary logic forms the basis of digital circuits, including processors and memory devices.
• Other Number Systems:
  • Besides binary (base-2), there are other numeral systems such as decimal (base-10), octal (base-8), and hexadecimal (base-16).
  • Conversions between these systems are essential for programming and system design.

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