Math Problem Statement

Solve 1011₂ =x₁₀

Solution

To solve 10112=x101011_2 = x_{10}, we need to convert the binary number 101121011_2 to its decimal (base 10) equivalent.

The binary number 101121011_2 can be expanded as follows: 10112=123+022+121+1201011_2 = 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0

Calculate each term: 123=81 \cdot 2^3 = 8 022=00 \cdot 2^2 = 0 121=21 \cdot 2^1 = 2 120=11 \cdot 2^0 = 1

Add them together to get the decimal equivalent: 8+0+2+1=118 + 0 + 2 + 1 = 11

Therefore, 10112=11101011_2 = 11_{10}

So, x=11x = 11.

Would you like more details or have any questions?

Here are 5 more questions you might find interesting:

  1. How do you convert a hexadecimal number to a decimal number?
  2. What is the process of converting a decimal number to a binary number?
  3. How do you add and subtract binary numbers?
  4. Can you explain the difference between binary and hexadecimal systems?
  5. How do you solve equations involving numbers in different bases?

Tip: Practice converting numbers between different bases to strengthen your understanding of number systems.

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Math Problem Analysis

Mathematical Concepts

Number Systems
Binary Numbers
Decimal Conversion

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9