Math Problem Statement

binary to decimal 7. 11110

Solution

To convert the binary number 11110211110_2 to decimal:

Each digit in a binary number represents a power of 2, starting from the rightmost digit (which represents 202^0).

So for 11110211110_2, we calculate:

111102=(1×24)+(1×23)+(1×22)+(1×21)+(0×20)11110_2 = (1 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (0 \times 2^0) =(1×16)+(1×8)+(1×4)+(1×2)+(0×1)= (1 \times 16) + (1 \times 8) + (1 \times 4) + (1 \times 2) + (0 \times 1) =16+8+4+2+0=30= 16 + 8 + 4 + 2 + 0 = 30

So, 11110211110_2 in decimal is 301030_{10}.

Would you like more details or have any questions?

Here are 5 related questions:

  1. How do you convert a larger binary number to decimal?
  2. What is the decimal equivalent of 10101210101_2?
  3. How do you convert a decimal number to binary?
  4. How can you perform binary addition?
  5. What are the common uses of binary numbers in computing?

Tip: Always start converting binary numbers from the rightmost digit, as it represents the smallest power of 2.

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Math Problem Analysis

Mathematical Concepts

Number Systems
Binary to Decimal Conversion

Formulas

Decimal = (b_n * 2^n) + (b_(n-1) * 2^(n-1)) + ... + (b_0 * 2^0)

Theorems

Positional Notation Theorem

Suitable Grade Level

Grades 5-7