Math Problem Statement

Convert the binary value 110000, start subscript, start subscript, 2, end subscript, end subscript1100002​​ into decimal.

Solution

To convert the binary value 1100002110000_2 into decimal, we break it down by powers of 2:

1100002=125+124+023+022+021+020110000_2 = 1 \cdot 2^5 + 1 \cdot 2^4 + 0 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 0 \cdot 2^0

Now, calculating each term:

125=321 \cdot 2^5 = 32 124=161 \cdot 2^4 = 16 023=00 \cdot 2^3 = 0 022=00 \cdot 2^2 = 0 021=00 \cdot 2^1 = 0 020=00 \cdot 2^0 = 0

Adding them together:

32+16+0+0+0+0=4832 + 16 + 0 + 0 + 0 + 0 = 48

Thus, the decimal equivalent of 1100002110000_2 is 4848.

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Related Questions:

  1. How do you convert decimal numbers to binary?
  2. What is the decimal value of 1011012101101_2?
  3. How do binary numbers work in computer memory?
  4. What is the process to convert binary numbers into hexadecimal?
  5. Can you convert 1100002110000_2 into octal?

Tip:

When converting binary to decimal, remember that each digit represents a power of 2, starting from 0 on the right.

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Math Problem Analysis

Mathematical Concepts

Binary to Decimal Conversion
Powers of Two

Formulas

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

Theorems

Positional Notation in Number Systems

Suitable Grade Level

Grades 6-8