Math Problem Statement

Convert the binary number 110111_2 to its decimal form.

Solution

The image shows the binary number 1101112110111_2.

To convert this binary number to its decimal (base 10) form, follow these steps:

  1. Label each binary digit (bit) with a power of 2, starting from the right (least significant bit). Each position corresponds to 2n2^n, where nn is the position index (starting from 0 on the right).

1101112=(125)+(124)+(023)+(122)+(121)+(120)110111_2 = (1 \cdot 2^5) + (1 \cdot 2^4) + (0 \cdot 2^3) + (1 \cdot 2^2) + (1 \cdot 2^1) + (1 \cdot 2^0)

  1. Calculate each term: 125=321 \cdot 2^5 = 32 124=161 \cdot 2^4 = 16 023=00 \cdot 2^3 = 0 122=41 \cdot 2^2 = 4 121=21 \cdot 2^1 = 2 120=11 \cdot 2^0 = 1

  2. Add the results: 32+16+0+4+2+1=5532 + 16 + 0 + 4 + 2 + 1 = 55

Thus, the binary number 1101112110111_2 is equivalent to 551055_{10} in decimal.

Do you need further details or have any questions? Here are some related topics:

  1. How do you convert decimal numbers to binary?
  2. What is the significance of each bit in a binary number?
  3. Can binary numbers be used to represent negative values?
  4. How do computers use binary numbers for calculations?
  5. What is the difference between binary, hexadecimal, and octal systems?

Tip: Always start binary conversions by assigning powers of 2, from right to left, for accuracy!

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Math Problem Analysis

Mathematical Concepts

Number Systems
Binary to Decimal Conversion

Formulas

Decimal value = Σ (binary digit * 2^position)

Theorems

Positional number system theorem

Suitable Grade Level

Grades 6-8