Introduction to Number Systems and Compression
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Questions and Answers

What is the base value for each of the following? (Select all that apply)

  • Binary (correct)
  • Octal
  • Hexadecimal (correct)
  • Decimal (correct)

Railways have devices called "axle counters" that count up how many train axles have passed by, and helps decide if a train has fully passed part of a track. However, because of a bug in the design of the axle counter logic, a train that has exactly 256 axles will result in a count of 0, and its existence will be ignored. Thus, trains that run on these buggy railways must have less than 256 axles. What is the most likely cause of this bug?

The axle counter is likely using a single byte (8 bits) to store the count, and since 256 is the maximum value that can be represented with 8 bits, the counter overflows and resets to 0.

How many bits are in 4 bytes?

32

Nora is learning to use image editing applications and doesn't understand when to lower the quality setting for JPEG saving. What's a good use case for using a lower quality setting?

<p>A good use case for a lower quality setting is when you want to reduce the file size of an image for online use or sharing. Lower quality settings can result in a much smaller file size, but they will also reduce the image quality.</p> Signup and view all the answers

Byte pair encoding is a compression algorithm that replaces the most common pairs of characters in a string with a character that isn't in the data, and creates a table of replacement mappings. Here's the output from a byte pair encoding: One ZY Two ZY Red ZY Blue ZY Is it possible to decode this?

<p>False (B)</p> Signup and view all the answers

Flashcards

Decimal

A counting system with a base of 10, using digits 0-9.

Binary

A counting system with a base of 2, using digits 0 and 1.

Hexadecimal

A counting system with a base of 16, using digits 0-9 and letters A-F.

Bit

A single unit of binary information, represented by a 0 or a 1.

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Byte

A group of 8 bits, typically used to represent a single character.

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Compression

The process of reducing the size of a file, often by removing redundant information.

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Lossless Compression

A compression technique that guarantees no loss of data during the process.

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Lossy Compression

A compression technique that removes some information, resulting in smaller file size but potential quality loss.

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Encryption

The process of converting information into a secret code using mathematical algorithms.

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Public Key

A key used to encrypt information, which can be shared publicly.

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Private Key

A key used to decrypt information, kept secret by the intended recipient.

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Expansion

The process of making data larger by converting it to a more detailed format.

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Conversion

The act of converting data from one counting system to another.

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Axle Counter

A technique used to determine if a train has completely passed a specific point on a track.

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Bug

A problem or error in the design or execution of a program or system.

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Octet

A group of 8 bits, which is the same as 1 byte.

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Digitization

The process of converting analog data, such as images or audio, into digital form.

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JPEG

A digital image format known for its compression techniques, allowing for smaller file sizes with potential quality loss.

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Quality Setting

The quality setting in a file saving dialog that determines how much data is compressed, affecting the resulting file size and visual quality.

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Byte Pair Encoding

A compression technique that replaces common pairs of characters with unique symbols, resulting in a smaller file size.

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Irreversible Compression

When the original data cannot be retrieved without loss of information.

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Reversible Compression

A form of compression where the original data can be perfectly restored from the compressed version.

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Bit Depth

The number of bits required to represent a value.

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Cryptography

The process of making data more secure by using mathematical algorithms to scramble it.

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Asymmetric Encryption

A type of encryption that uses both a public key and a private key.

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Symmetric Encryption

A type of encryption that uses the same key for both encryption and decryption.

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Cipher

A specific set of rules used in cryptography for encryption and decryption.

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Multifunctionality

The ability to use a system or device for multiple purposes.

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Modulation

The process of converting digital information into a continuous signal, suitable for transmission over analog channels.

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Character Encoding

A standard method for representing text characters using a set of numbers.

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Dictionary Compression

A type of data compression that uses a series of symbols stored in a dictionary to represent repeated patterns.

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Huffman Coding

A type of compression that analyzes the frequency of occurrence of data and assigns shorter codes to more frequent elements.

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Study Notes

Section 1

  • Counting systems include decimal (base 10), binary (base 2), and hexadecimal (base 16).
  • Each counting system has a unique base.
  • A digit increments until it reaches its maximum value, then resets to 0 and increments the next place value.
  • Binary numbers are often grouped into 8-bit units called bytes.
  • A byte can hold 256 possible values (0-255). More bits are needed for values larger than 255.
  • Different counting systems can be converted to each other with specific methods.

Section 2

  • Compression methods include lossless and lossy.
  • Lossless compression preserves all original data.
  • Lossy compression removes unnecessary data for smaller file sizes.
  • Lossy compression can result in significantly smaller file sizes than lossless compression.
  • Cryptography and encryption involve using keys to encode and decode.
  • Stronger encryption uses more bits.
  • Encryption allows for secure information exchange between parties, using public and private keys.

Question 1

  • Decimal: base 10
  • Binary: base 2
  • Hexadecimal: base 16

Question 2

  • The axle counter bug likely uses modulo 256 arithmetic. With this, the count of 256 is treated as zero.

Question 3

  • 4 bytes * 8 bits/byte = 32 bits

Question 4

  • Lower quality JPEG settings are suitable for certain image types where minor loss of quality is acceptable.
  • Examples include less detailed images or images intended for display on a small screen.

Question 5

  • The output "One ZY Two ZY Red ZY Blue ZY" is a sequence of byte pairs that have been compressed.
  • Determining the original string requires access to the byte pair encoding algorithm/mapping table, which is not provided.
  • Without the table to decode which pairs relate to text, the original string cannot be reconstructed.

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Description

This quiz covers essential concepts of counting systems such as decimal, binary, and hexadecimal. It also delves into data compression techniques, including lossless and lossy methods, as well as the fundamentals of cryptography and encryption. Test your understanding of these critical topics in computer science!

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