Math Problem Statement

Convert 1100011100111 to hindu arabic number

Solution

The binary number 1100011100111 can be converted to its equivalent Hindu-Arabic number (decimal) by following these steps:

  1. Write the binary number:
    1100011100111

  2. Assign powers of 2 to each digit, starting from the right (starting with 202^0):
    1212+1211+0210+029+028+127+126+125+024+023+122+121+1201 \cdot 2^{12} + 1 \cdot 2^{11} + 0 \cdot 2^{10} + 0 \cdot 2^{9} + 0 \cdot 2^{8} + 1 \cdot 2^{7} + 1 \cdot 2^{6} + 1 \cdot 2^{5} + 0 \cdot 2^{4} + 0 \cdot 2^{3} + 1 \cdot 2^{2} + 1 \cdot 2^{1} + 1 \cdot 2^{0}

  3. Evaluate the powers of 2:
    =14096+12048+01024+0512+0256+1128+164+132+016+08+14+12+11= 1 \cdot 4096 + 1 \cdot 2048 + 0 \cdot 1024 + 0 \cdot 512 + 0 \cdot 256 + 1 \cdot 128 + 1 \cdot 64 + 1 \cdot 32 + 0 \cdot 16 + 0 \cdot 8 + 1 \cdot 4 + 1 \cdot 2 + 1 \cdot 1

  4. Sum the values:
    4096+2048+128+64+32+4+2+1=63754096 + 2048 + 128 + 64 + 32 + 4 + 2 + 1 = 6375

So, the binary number 1100011100111 is equal to the Hindu-Arabic number 6375.

Would you like more details or have any questions?

Here are five related questions:

  1. How do you convert decimal numbers to binary?
  2. What is the binary representation of the decimal number 255?
  3. How does binary addition work?
  4. How do binary numbers apply in computer systems?
  5. How do you convert octal numbers to decimal?

Tip: When converting binary to decimal, always start assigning powers of 2 from the rightmost digit.

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Math Problem Analysis

Mathematical Concepts

Binary to Decimal Conversion
Number Systems

Formulas

Binary to Decimal Conversion: sum of binary digits (0 or 1) times powers of 2
Formula: n = b₁ × 2⁰ + b₂ × 2¹ + b₃ × 2² + …

Theorems

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Suitable Grade Level

Grades 6-8