Math Problem Statement
Convert the following base 2 numeral to a base 10 numeral: 101110 (Base 2).
Solution
The given problem asks to convert the binary (base 2) number 101110
to a decimal (base 10) number.
Here’s the step-by-step conversion:
- Write out the binary number:
- Assign powers of 2 to each digit from right to left:
- Evaluate the powers of 2:
- Add the values:
Thus, the decimal (base 10) equivalent of 101110_2
is 46.
Would you like a detailed explanation on any step?
Here are 5 related questions to expand your understanding:
- How do you convert a binary number with more digits to a decimal number?
- What is the reverse process of converting a decimal number to binary?
- How are binary numbers used in computing systems?
- Can binary numbers represent negative values, and how?
- What is the significance of binary arithmetic in digital electronics?
Tip: Remember, each binary digit (bit) represents a power of 2, starting from on the right.
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Math Problem Analysis
Mathematical Concepts
Binary to Decimal Conversion
Powers of 2
Formulas
Decimal = Sum of (Binary Digit * 2^Position)
Theorems
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Suitable Grade Level
Grades 5-7