Math Problem Statement

Write the number given below as a decimal numeral. 1110two

Solution

The number 111021110_2 is a binary number. To convert it to a decimal numeral, we follow these steps:

  1. Write the binary number 111021110_2 with its digits and their place values: 11102=123+122+121+0201110_2 = 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0

  2. Calculate the powers of 2 for each position: =18+14+12+01= 1 \cdot 8 + 1 \cdot 4 + 1 \cdot 2 + 0 \cdot 1

  3. Add the results: =8+4+2+0=14= 8 + 4 + 2 + 0 = 14

So, the decimal equivalent of 111021110_2 is 1414.

Would you like more details or have any questions?

Here are 5 related questions:

  1. How do you convert a binary number to decimal in general?
  2. What is the decimal value of 101121011_2?
  3. How do you convert a decimal number back to binary?
  4. What is the binary representation of the decimal number 2525?
  5. How does the binary number system differ from the decimal system?

Tip: When converting binary to decimal, always start from the rightmost digit and assign increasing powers of 2 from right to left.

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Math Problem Analysis

Mathematical Concepts

Binary Number System
Decimal Conversion

Formulas

Decimal equivalent of binary = Sum of (digit × 2^position) for each binary digit

Theorems

Positional number system

Suitable Grade Level

Grades 6-8