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Questions and Answers
What power of 2 does the leftmost digit represent in a binary number?
What power of 2 does the leftmost digit represent in a binary number?
Which of the following number systems is most commonly used in human contexts?
Which of the following number systems is most commonly used in human contexts?
What is the decimal equivalent of the binary number 1010?
What is the decimal equivalent of the binary number 1010?
Which digits are used in the octal number system?
Which digits are used in the octal number system?
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In hexadecimal, which digit represents the decimal value of 10?
In hexadecimal, which digit represents the decimal value of 10?
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What is the sum of the decimal equivalent values of octal number 52?
What is the sum of the decimal equivalent values of octal number 52?
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How many digits are employed in the hexadecimal number system?
How many digits are employed in the hexadecimal number system?
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Which computer number system was historically used for machine code and memory addresses?
Which computer number system was historically used for machine code and memory addresses?
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What is the binary representation of the decimal number 348?
What is the binary representation of the decimal number 348?
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When converting the decimal number 348 to hexadecimal, what is the remainder after the first division by 16?
When converting the decimal number 348 to hexadecimal, what is the remainder after the first division by 16?
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What is the result of the binary multiplication $110 imes 101$?
What is the result of the binary multiplication $110 imes 101$?
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What is the decimal equivalent of the hexadecimal number 1A7?
What is the decimal equivalent of the hexadecimal number 1A7?
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What remains when dividing the binary number $101110111$ by $1011$?
What remains when dividing the binary number $101110111$ by $1011$?
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Which of the following binary division operations requires special consideration due to being undefined?
Which of the following binary division operations requires special consideration due to being undefined?
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Which of the following correctly describes the carry-over process in binary addition?
Which of the following correctly describes the carry-over process in binary addition?
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What is the result of the binary addition $101101 + 111101$?
What is the result of the binary addition $101101 + 111101$?
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What is the quotient when $11011$ is divided by $101$?
What is the quotient when $11011$ is divided by $101$?
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What will be the result of multiplying $1$ by $1$ in binary?
What will be the result of multiplying $1$ by $1$ in binary?
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Which of the following binary numbers is NOT a correct representation of decimal 19?
Which of the following binary numbers is NOT a correct representation of decimal 19?
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What is the correct octal representation of the decimal number 348?
What is the correct octal representation of the decimal number 348?
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In binary subtraction, when do you need to borrow?
In binary subtraction, when do you need to borrow?
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Study Notes
Computer Number Systems
- Computer number systems are used to represent and work with numbers in digital computing.
- These systems are essential for data encoding, calculations, and communication within and across digital devices.
- The four primary computer number systems are binary, decimal, octal, and hexadecimal.
Binary Number System (Base-2)
- Binary is the fundamental number system in computing.
- It uses only two digits: 0 and 1.
- Each digit in a binary number represents a power of 2.
- The rightmost digit represents 20 (1), the next digit to the left represents 21 (2), the next 22 (4), and so on.
- Binary numbers are used in all digital devices and computer systems to represent data and perform logical operations like addition, subtraction, and bitwise operations.
- Example: Binary 1010 represents 1 * 23 + 0 * 22 + 1 * 21 + 0 * 20 = 10 in decimal.
Decimal Number System (Base-10)
- Decimal is the number system most commonly used by humans.
- It employs ten digits: 0 to 9.
- Each digit in a decimal number represents a power of 10.
- The rightmost digit represents 100 (1), the next digit to the left represents 101 (10), the next 102 (100), and so on.
- Decimal numbers are used for everyday calculations, mathematics, and most human-oriented contexts.
- Example: Decimal 345 represents 3 * 102 + 4 * 101 + 5 * 100 = 345.
Octal Number System (Base-8)
- Octal uses eight digits: 0 to 7.
- Each digit represents a power of 8.
- The rightmost digit represents 80 (1), the next 81 (8), next 82 (64), and so on.
- Octal numbers are less common in modern computing but were historically used to represent machine code and memory addresses.
- Example: Octal 52 represents 5 * 81 + 2 * 80 = 42 in decimal.
Hexadecimal Number System (Base-16)
- Hexadecimal employs sixteen digits: 0 to 9, and A to F (A=10, B=11, C=12, D=13, E=14, F=15).
- Each digit represents a power of 16.
- The rightmost digit represents 160 (1), the next 161 (16), the next 162 (256), and so on.
- Hexadecimal numbers are widely used in computing for representing binary data compactly and memory addresses.
- Example: Hexadecimal 1A7 represents 1 * 162 + 10 * 161 + 7 * 160 = 423 in decimal.
Converting Decimals to Other Number Systems
- Decimal to Binary: Repeated division by 2.
- Decimal to Octal: Repeated division by 8.
- Decimal to Hexadecimal: Repeated division by 16.
Arithmetic Operations on Binary Numbers
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Binary Addition: Follows the same rules as decimal addition but carries over when the sum is 2 (not 10).
- 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 0 (carry-over 1).
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Binary Subtraction: Similar to decimal subtraction but borrows when the minuend is smaller than the subtrahend.
- 0 - 0 = 0, 1 - 0 = 1, 1 - 1 = 0, 0 - 1 = Borrow.
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Binary Multiplication: Similar to decimal multiplication but only involves 0 and 1.
- 0 * 0 = 0, 0 * 1 = 0, 1 * 0 = 0, 1 * 1 = 1.
-
Binary Division: Similar to decimal division, involving a dividend, divisor, quotient, and remainder.
- 0 ÷ 1 = 0 remainder 0, 1 ÷ 1 = 1 remainder 0, 0 ÷ 0 = undefined, 1 ÷ 0 = undefined.
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Description
Test your knowledge on various computer number systems including binary, decimal, octal, and hexadecimal. Understand their significance in data encoding and calculations within digital devices. This quiz covers the fundamentals and applications of these essential systems.
