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Questions and Answers
Which numbering system uses digits 0 to 7?
Which numbering system uses digits 0 to 7?
What is the base of the hexadecimal number system?
What is the base of the hexadecimal number system?
Which of the following represents a signed integer?
Which of the following represents a signed integer?
What is true about unsigned integers?
What is true about unsigned integers?
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Which data representation is not typically associated with machine instructions?
Which data representation is not typically associated with machine instructions?
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What is the maximum value represented by a 5-bit unsigned binary number?
What is the maximum value represented by a 5-bit unsigned binary number?
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Which binary representation method uses the most significant bit as a sign digit?
Which binary representation method uses the most significant bit as a sign digit?
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What is the correct 6-bit one's complement representation for -10?
What is the correct 6-bit one's complement representation for -10?
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Which coding system is designed to eventually replace ASCII as the primary text-coding system?
Which coding system is designed to eventually replace ASCII as the primary text-coding system?
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What is the range of an unsigned binary number represented with n bits?
What is the range of an unsigned binary number represented with n bits?
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Study Notes
Computer Fundamentals - Number Systems
- The presentation introduces four number systems: binary, octal, decimal, and hexadecimal.
- It discusses conversions between these systems, along with representations of signed and unsigned numbers.
Data, Program and Information
- A number is a string of one or more digits used for counting, quantifying, and measuring.
- A digit is a single numerical symbol of a number, or the smallest symbol of numbers.
Number Systems - Types
- Binary (base 2): Uses only 0 and 1.
- Octal (base 8): Uses digits 0-7.
- Decimal (base 10): Uses digits 0-9.
- Hexadecimal (base 16): Uses digits 0-9 and A-F.
Positional Number System
- Each digit in a number has a value based on its position.
- In decimal, the value of each digit is multiplied by increasing powers of 10.
Decimal Number System
- Represents numbers using decimal digits (0-9).
- Each digit's position determines its power of 10 multiplier.
- Example: 83 = (8 x 101) + (3 x 100).
- Applies to both integers and fractions (negative exponents).
Decimal Number System - Most & Least Significant Digits
- The leftmost digit is the most significant digit (highest value).
- The rightmost digit is the least significant digit (lowest value).
- Example: 3501.51 -> 3 (most significant) , 1 (least significant)
Binary Number System
- Uses only two digits: 0 and 1.
- Each digit's position determines its power of 2 multiplier.
- Example: 102 = (1 * 21) + (0 * 20) = 210
- Often uses subscripts (2) to indicate binary representation (e.g., 10012).
Binary Number System - Conversion to Decimal
- Convert binary to decimal by adding the weights of each digit with a value of 1, based on its position (powers of 2).
- Example: 001010102 = 020 + 121 + 022 + 123 + 024 + 125 + 026 + 027 = 4210
Binary Number System - Conversion from Decimal
- Divide the decimal number by 2 repeatedly, recording the remainders.
- The remainders, read in reverse order form, are the binary equivalents.
- Example: 7510 converts to 10010112
Hexadecimal Number System
- Shortens binary representations to be more human-readable.
- Uses digits 0-9 and A-F, where A=10, B=11, C=12, D=13, E=14, F=15.
- Example: 1AF16 = 1⋅162 + 10⋅161 + 15⋅160 = 43110.
Hexadecimal to Decimal Conversion
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- Convert the hexadecimal number to binary
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- Convert binary to decimal (using the powers of 2 method)
Octal Number System
- Uses digits 0-7.
- Each position multiplies its digit by increasing powers of 8
Signed and Unsigned Integers
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Unsigned: Represents only positive values.
- The range of an N-bit unsigned integer is from 0 to 2N - 1.
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Signed: Represents both positive and negative values. Common approaches include sign-magnitude, one's complement, and two's complement.
- Two's complement is the common method. The MSB acts as a sign bit.
Coding Systems for Text-Based Data
- ASCII (American Standard Code for Information Interchange): Used primarily with personal computers.
- EBCDIC (Extended Binary-Coded Decimal Interchange Code): Primarily used for mainframes.
- Unicode: A universal coding standard replacing ASCII in many applications. Includes UTF-8, UTF-16, and UTF-32.
Coding Systems for Other Data Types
- Images (pixels): Use different numbers of bits depending on the color depth (e.g., 16-color, 256-color, True Color).
- Audio: Typically involves converting analog audio signals to digital bits using Analog-to-Digital (ADC) converters, and then back to analog for output by Digital-to-Analog (DAC) converters.
- Video: Can represent images using bits and pixel codes.
- Machine Language: Uses binary codes to represent machine operations.
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Description
This quiz covers the essential number systems, including binary, octal, decimal, and hexadecimal. It explores conversions between these systems along with the principles of signed and unsigned numbers, emphasizing the significance of positional notation in determining a digit's value.
