Math Problem Statement

10110011010 to octal

Solution

To convert the binary number 1011001101010110011010 to octal, follow these steps:

  1. Group the binary digits into groups of 3, starting from the right. If the leftmost group has fewer than 3 digits, pad it with zeros.

    1011001101001011001101010110011010 \rightarrow 010 110 011 010

  2. Convert each group of 3 binary digits to its octal equivalent:

    • 0102=28010_2 = 2_8
    • 1102=68110_2 = 6_8
    • 0112=38011_2 = 3_8
    • 0102=28010_2 = 2_8
  3. Write the octal equivalent by combining the results:

    The octal representation of 10110011010210110011010_2 is 263282632_8.


Would you like more details on any of the steps, or have any questions about this process?

Additional Questions:

  1. How do you convert between binary and hexadecimal?
  2. Can you explain how to convert from octal to binary?
  3. What is the significance of padding zeros when grouping binary digits?
  4. How would you convert a floating-point binary number to octal?
  5. What are the differences between binary, octal, and hexadecimal number systems?

Tip: Always pad your binary number to the left with zeros if the grouping of 3 is not even, to avoid errors in conversion!

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Math Problem Analysis

Mathematical Concepts

Binary to Octal Conversion

Formulas

Group binary digits into groups of 3, convert each group to its octal equivalent

Theorems

Binary to octal conversion rule

Suitable Grade Level

Grades 5-7