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:

  1. Write out the binary number: 1011102101110_2
  2. Assign powers of 2 to each digit from right to left: 1011102=125+024+123+122+121+020101110_2 = 1 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0
  3. Evaluate the powers of 2: =132+016+18+14+12+01= 1 \cdot 32 + 0 \cdot 16 + 1 \cdot 8 + 1 \cdot 4 + 1 \cdot 2 + 0 \cdot 1
  4. Add the values: =32+0+8+4+2+0=46= 32 + 0 + 8 + 4 + 2 + 0 = 46

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:

  1. How do you convert a binary number with more digits to a decimal number?
  2. What is the reverse process of converting a decimal number to binary?
  3. How are binary numbers used in computing systems?
  4. Can binary numbers represent negative values, and how?
  5. What is the significance of binary arithmetic in digital electronics?

Tip: Remember, each binary digit (bit) represents a power of 2, starting from 202^0 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