Introduction to Number Systems and Compression

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

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?

How many bits are in 4 bytes?

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?

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?

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.

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!