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Questions and Answers
Which number system has a base of 2?
The octal number system consists of digits from 0 to 9.
False
What are the 16 symbols used in the hexadecimal number system?
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
The decimal number system consists of ___ digits.
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Match the following number systems with their correct base:
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When converting from decimal to binary, which step comes first?
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The binary number system can represent 10 different values.
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What is the base of the octal number system?
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What is the first step in converting a decimal number to hexadecimal?
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To convert binary to octal directly, you group binary digits in sets of four.
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What does LSD stand for in the context of converting decimal to hexadecimal?
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The binary number (11011)2 is equivalent to (____)10.
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Match the following methods of conversion to their descriptions:
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Which method is effective for converting binary directly to hexadecimal?
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When converting a fractional decimal number, the whole number should be removed after each multiplication step.
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The octal equivalent of the binary number (101111)2 is (____)8.
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What is the binary equivalent of the octal number (75)8?
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In the sign magnitude representation, negative numbers are represented with a sign bit of 0.
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What is the decimal equivalent of the octal number (75)8?
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The binary representation of +5 in sign magnitude format is ___.
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Which method is used to convert from octal to hexadecimal?
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Match the following representations with their example:
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In one’s complement, the negative numbers are represented identically to positive numbers.
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What prefix is commonly used to denote binary numbers?
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Study Notes
Data Representation
- Data representation refers to the techniques used to represent data in computers.
- Number systems are fundamental to computer design and organization.
- Computers use four main number systems: Decimal, Binary, Octal, and Hexadecimal.
Decimal Number System
- The decimal system uses ten digits (0-9) and has a base of 10.
- Examples of decimal numbers include 405 and 145.25.
Binary Number System
- The binary system uses only two digits (0 and 1), with a base of 2.
- Computers operate based on two states (on/off) and store information using these states.
- Examples of binary numbers include 101 and 1001.11.
Octal Number System
- The octal system uses eight digits (0-7), with a base of 8.
- Examples of octal numbers include 76 and 55.25.
Hexadecimal Number System
- The hexadecimal system, often called 'Hex', uses 16 symbols (0-9 and A-F) and has a base of 16.
- Examples of hexadecimal numbers include 45 and 11A.
Conversion between Number Systems
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Converting Decimal to Binary:
- Repeatedly divide the decimal number by 2.
- Note the remainders.
- Arrange the remainders in reverse order (the first remainder is the least significant digit, the last is the most significant digit).
-
Converting Binary to Decimal:
- Assign weights (powers of 2) to each bit, starting from the rightmost with 2^0.
- Multiply each bit by its corresponding weight.
- Sum the results to get the decimal equivalent.
-
Converting Decimal to Octal:
- Repeatedly divide the decimal number by 8.
- Note the remainders.
- Arrange the remainders in reverse order.
-
Converting Octal to Decimal:
- Assign weights (powers of 8) to each digit, starting from the rightmost with 8^0.
- Multiply each digit by its corresponding weight.
- Sum the results to get the decimal equivalent.
-
Converting Decimal to Hexadecimal:
- Repeatedly divide the decimal number by 16.
- Note the remainders.
- Arrange the remainders in reverse order.
- Convert any remainders above 9 to their corresponding hexadecimal letters (A-F).
-
Converting Binary to Octal:
- Group the binary digits into groups of 3 (from right to left for integers, left to right for fractions)
- Convert each group into its decimal equivalent.
- If a group has less than 3 bits, add leading zeros to complete the group.
-
Converting Binary to Hexadecimal:
- Group the binary digits into groups of 4 (from right to left for integers, left to right for fractions).
- Convert each group into its decimal equivalent.
- If a group has less than 4 bits, add leading zeros to complete the group.
-
Converting Octal to Binary:
- Convert each digit of the octal number into its 3-bit binary equivalent.
-
Converting Octal to Hexadecimal:
- Convert the octal number to binary.
- Group the binary digits into groups of 4.
- Convert each group to its hexadecimal equivalent.
-
Converting Hexadecimal to Decimal:
- Assign weights (powers of 16) to each digit, starting from the rightmost with 16^0.
- Multiply each digit by its corresponding weight.
- Sum the results to get the decimal equivalent.
-
Converting Hexadecimal to Binary:
- Convert each digit of the hexadecimal number to its 4-bit binary equivalent.
Binary representation of integers
- There are three main ways to represent positive and negative integers in binary:
- Sign magnitude: a sign bit (0 for positive, 1 for negative) is added to the left of the magnitude, represented as a simple binary number.
- One's Complement: positive numbers are represented as usual in signed magnitude. Negative numbers are represented by inverting (flipping) all the bits of the positive equivalent.
- Two's Complement: positive numbers are represented as usual in signed magnitude. Negative numbers are obtained by adding 1 to the one's complement representation.
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Description
This quiz covers key concepts in data representation, focusing on various number systems used in computing, including Decimal, Binary, Octal, and Hexadecimal. Test your understanding of these systems and their significance in computer organization.
