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Convert the hexadecimal number F3A7C2 to binary, octal and decimal.

Question

Convert the hexadecimal number F3A7C2 to binary, octal and decimal.

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Solution

Sure, let's convert the hexadecimal number F3A7C2 to binary, octal, and decimal.

  1. Hexadecimal to Binary: Each hexadecimal digit can be converted to a 4-digit binary number. Here's how you convert F3A7C2:
  • F = 1111
  • 3 = 0011
  • A = 1010
  • 7 = 0111
  • C = 1100
  • 2 = 0010

So, F3A7C2 in binary is 111100111010011111000010.

  1. Hexadecimal to Octal: First, convert the hexadecimal number to binary, then group the binary number into sets of three (from right to left), and convert each group to its octal equivalent.
  • 111100111010011111000010 = 111 100 111 010 011 111 000 010
  • 111 = 7, 100 = 4, 111 = 7, 010 = 2, 011 = 3, 111 = 7, 000 = 0, 010 = 2

So, F3A7C2 in octal is 747273702.

  1. Hexadecimal to Decimal: Each hexadecimal digit can be multiplied by 16^n, where n is the position of the digit (counting from right to left, starting from 0), and then summed.
  • F = 15 * (16^5) = 15728640
  • 3 = 3 * (16^4) = 196608
  • A = 10 * (16^3) = 163840
  • 7 = 7 * (16^2) = 1792
  • C = 12 * (16^1) = 192
  • 2 = 2 * (16^0) = 2

So, F3A7C2 in decimal is 15728640 + 196608 + 163840 + 1792 + 192 + 2 = 15990574.

This problem has been solved

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