Math Problem Statement
110110000010110_2 A. 27x2^(10)+22 B. 27×2^(10)+ 44 C. 27×2^(11) +22 D.27×2^(11)+44
Solution
To solve this problem, we need to interpret the binary number and convert it into its decimal (base-10) equivalent.
The binary number can be expanded as follows:
Calculating powers of 2:
Adding these together:
Now, comparing this with the given options:
- Option A:
- Option B:
- Option C:
- Option D:
The correct match is Option B: .
Would you like further details or have any questions?
Here are 5 related questions to expand on this:
- How do you convert a binary number to decimal manually?
- What are the common uses of binary numbers in computing?
- How can powers of two be computed quickly?
- What is the significance of base-2 in digital systems?
- How does understanding binary assist in understanding machine code?
Tip: When working with binary numbers, remember each digit represents an increasing power of 2, starting from the rightmost digit (which is ).
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Binary to Decimal Conversion
Powers of 2
Algebraic Expressions
Formulas
Binary to Decimal Conversion: \(1 \times 2^n + 0 \times 2^{n-1} + \dots + 1 \times 2^0\)
Powers of 2
Algebraic Expressions: a × 2^n + b
Theorems
-
Suitable Grade Level
Grades 10-12