Math Problem Statement
Solution
The notebook page shows the conversion of binary numbers to decimal numbers. Let's break down each step as shown in the image:
(a) Conversion of 110111₂ to decimal:
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The binary number 110111₂ is converted to decimal by expanding it using powers of 2:
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Calculating the powers of 2:
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Summing all the values:
So, .
(b) Conversion of 11100011₂ to decimal:
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The binary number 11100011₂ is converted to decimal by expanding it using powers of 2:
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Calculating the powers of 2:
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Summing all the values:
So, .
Let me know if you want further details or if you have any questions!
Related Questions:
- How do you convert a decimal number to binary?
- What is the significance of each digit in a binary number?
- How can binary numbers be used in computer systems?
- What is the process for converting binary numbers to hexadecimal?
- How can you check if a binary number is correct after conversion?
Tip: Always double-check each step when converting between number systems to ensure accuracy, especially when dealing with larger binary numbers.
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Math Problem Analysis
Mathematical Concepts
Number Systems
Binary to Decimal Conversion
Formulas
Decimal value of binary number = Sum of (binary digit × 2^position)
Theorems
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Suitable Grade Level
Grades 6-8
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