Math Problem Statement

convert the following

Convert the following numbers between Decimal, Binary, Octal, and Hexadecimal systems.

Solution

The assignment image shows a table where conversions between different number systems (Decimal, Binary, Octal, and Hexadecimal) are required. Some values are already filled in the table, such as:

  • Decimal: 74
  • Binary: 110110
  • Octal: 62
  • Hexadecimal: A2B

Let's proceed with the conversions to complete the table.

1. Decimal: 74

  • Binary: 7410=1001010274_{10} = 1001010_2
  • Octal: 7410=112874_{10} = 112_8
  • Hexadecimal: 7410=4A1674_{10} = 4A_{16}

2. Binary: 110110

  • Decimal: 1101102=5410110110_2 = 54_{10}
  • Octal: 1101102=668110110_2 = 66_8
  • Hexadecimal: 1101102=3616110110_2 = 36_{16}

3. Octal: 62

  • Decimal: 628=501062_8 = 50_{10}
  • Binary: 628=110010262_8 = 110010_2
  • Hexadecimal: 628=321662_8 = 32_{16}

4. Hexadecimal: A2B

  • Decimal: A2B16=260310A2B_{16} = 2603_{10}
  • Binary: A2B16=1010001010112A2B_{16} = 101000101011_2
  • Octal: A2B16=50458A2B_{16} = 5045_8

This completes the table. Let me know if you'd like to see any detailed steps for the conversions, or if you have any other questions!


Here are 5 questions related to this task:

  1. How do you convert a number from binary to decimal?
  2. What is the significance of the hexadecimal system in computing?
  3. How do you perform conversions between octal and hexadecimal systems?
  4. What are the practical uses of different number systems in computer science?
  5. How can you verify if a binary to octal conversion is correct?

Tip: Always double-check conversions by reversing the process. For example, after converting from decimal to binary, convert the binary back to decimal to verify your result.

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Math Problem Analysis

Mathematical Concepts

Number Systems
Base Conversions
Binary
Octal
Hexadecimal

Formulas

Binary to Decimal: Sum of (bit * 2^position)
Decimal to Binary: Repeated division by 2, recording remainders
Decimal to Octal: Repeated division by 8, recording remainders
Decimal to Hexadecimal: Repeated division by 16, recording remainders

Theorems

Place Value Theorem for Positional Number Systems

Suitable Grade Level

Grade 10