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Questions and Answers
What is the binary representation of the decimal number 4?
What is the binary representation of the decimal number 4?
How many bits are used to represent the number 4 in binary?
How many bits are used to represent the number 4 in binary?
Which of the following represents the Most Significant Bit (MSB) in the binary number 100₂?
Which of the following represents the Most Significant Bit (MSB) in the binary number 100₂?
Which operation is performed repeatedly to convert the decimal number 4 into binary?
Which operation is performed repeatedly to convert the decimal number 4 into binary?
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What does the term 'bit' refer to in binary numbers?
What does the term 'bit' refer to in binary numbers?
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In the binary representation of 4, how many zeros are present?
In the binary representation of 4, how many zeros are present?
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In which base is the binary number system represented?
In which base is the binary number system represented?
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Which binary number corresponds to the decimal number 14?
Which binary number corresponds to the decimal number 14?
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What is the value of the binary number 1010 in decimal?
What is the value of the binary number 1010 in decimal?
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How is the decimal number 1235 represented using powers of 10?
How is the decimal number 1235 represented using powers of 10?
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What is the binary representation of the decimal number 25?
What is the binary representation of the decimal number 25?
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Which of the following statements about binary numbers is incorrect?
Which of the following statements about binary numbers is incorrect?
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Which statement distinguishes the binary number system from the decimal system?
Which statement distinguishes the binary number system from the decimal system?
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Study Notes
Understanding Binary
- Binary is a numbering system that uses only two digits: 0 and 1.
- It is foundational to digital encoding systems, reflecting two possible states.
- The binary number system operates in base-2, with each digit called a bit.
Converting Decimal to Binary
- To convert a decimal number to binary, divide the number by 2 repeatedly until reaching 0, recording the remainders.
- Example for decimal number 4:
- 4 divided by 2 yields a quotient of 2 and a remainder of 0.
- 2 divided by 2 yields a quotient of 1 and a remainder of 0.
- 1 divided by 2 yields a quotient of 0 and a remainder of 1.
- Collecting remainders in reverse order gives binary 100₂.
Bit Significance
- In binary representation, the Least Significant Bit (LSB) is the rightmost bit while the Most Significant Bit (MSB) is the leftmost bit.
- For binary 100₂, LSB is 0 and MSB is 1.
- Total bits for the number 4 in binary is 3, represented as 100₂.
Binary Representation of Decimal Numbers
- Binary numbers for decimals 1 to 25:
- 1 = 1, 2 = 10, 3 = 11, 4 = 100, 5 = 101
- 6 = 110, 7 = 111, 8 = 1000, 9 = 1001, 10 = 1010
- 11 = 1011, 12 = 1100, 13 = 1101, 14 = 1110, 15 = 1111
- 16 = 10000, 17 = 10001, 18 = 10010, 19 = 10011, 20 = 10100
- 21 = 10101, 22 = 10110, 23 = 10111, 24 = 11000, 25 = 11001
Decimal System vs Binary System
- Decimal operates in base 10 using digits 0-9, while binary operates in base 2 using digits 0-1.
- The term radix refers to the base of a numerical system.
- A decimal number is expressed as a weighted sum of powers of 10 (ex: 1235 = 1×10³ + 2×10² + 3×10¹ + 5×10⁰).
Conversion Methodology
- To illustrate place values:
- 10³ represents thousands, 10² represents hundreds, 10¹ represents tens, and 10⁰ represents ones.
- Converting from decimal to binary involves both division and understanding of positional values in respective bases.
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Description
Explore the fundamentals of the binary number system with this quiz. Understand how binary notation works, how it applies to digital encoding, and the relationship between binary digits and their values. Test your knowledge of the base-2 system and its significance in computing.
