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Questions and Answers
What is the base of the Decimal number system?
What is the base of the Decimal number system?
In a binary number system, the digits used are 0 and 1.
In a binary number system, the digits used are 0 and 1.
True
What is a nybble?
What is a nybble?
4 bits
What is the highest digit used in the hexadecimal number system?
What is the highest digit used in the hexadecimal number system?
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A byte consists of ______ bits.
A byte consists of ______ bits.
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What is the two's complement of the binary number 01010100100?
What is the two's complement of the binary number 01010100100?
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1K (kilo or ‘kibi’) = ______
1K (kilo or ‘kibi’) = ______
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Which number system uses the digits 0-9 and A-F?
Which number system uses the digits 0-9 and A-F?
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In the binary number system, digit b0 is the most significant bit (MSB).
In the binary number system, digit b0 is the most significant bit (MSB).
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What is the value of 4 + 8 in hexadecimal?
What is the value of 4 + 8 in hexadecimal?
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Study Notes
Base-N Number System
- Base N represents a number system with N unique digits.
- Digits range from 0 to N - 1.
- Positional number system assigns a value to each digit based on its position.
- The digit at the rightmost position is the Least Significant Digit (LSD) and the digit at the leftmost position is the Most Significant Digit (MSD).
Decimal Number System
- Uses base 10 with ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- Also a positional number system.
Binary Number System
- Uses base 2 with two digits: 0, 1.
- Binary digits are called bits.
- The rightmost bit is the Least Significant Bit (LSB) and the leftmost bit is the Most Significant Bit (MSB).
Definitions
- Nybble: 4 bits
- Byte: 8 bits
- Short word: 2 bytes (16 bits)
- Double word: 4 bytes (32 bits)
- Long word: 8 bytes (64 bits)
- 1k (kilo): 1,024
- 1M (mega): 1,048,576
- 1G (giga): 1,073,741,824
Hexadecimal Number System
- Uses base 16 with sixteen digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
- Also a positional number system.
Binary Addition
- The single bit addition table guides addition with a carry if the sum is 2 or more.
Hex Addition
- 4-bit addition is used with carry when the sum exceeds F.
Hex Digit Addition Table
- Summarizes all possible hex digit additions, including carryovers for sums exceeding F.
1’s Complements
- Calculated by inverting each bit (0 becomes 1, 1 becomes 0).
2’s Complements
- Calculated by first taking the 1’s complement and then adding 1.
Complements
- The 2’s complement of the 2’s complement of a number results in the original number.
Two's Complement Representation for Signed Numbers
- Two’s complement notation is used to represent negative numbers.
- Two’s complement encoding is done by taking the 2’s complement of the positive value.
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Description
Explore the various base-N number systems, including decimal, binary, and hexadecimal. This quiz covers the key concepts, definitions, and properties of each system, such as unique digits and positional notation. Test your knowledge on how these systems function and their significance in computing.
