Data Storage and Compression - Measuring Data Capacity

This section explores how the amount of data a storage device can hold is measured. Understanding these concepts is fundamental to computer science.

Units of Measurement

Data storage is typically measured using units that represent different quantities of information. The most common units are:

• Bit (b): The smallest unit of data. A bit can have one of two values: 0 or 1.
• Byte (B): A group of 8 bits. $$1 \text{ Byte} = 8 \text{ bits}$$
• Kilobyte (KB): $$1 \text{ KB} = 1024 \text{ Bytes} = 2^{10} \text{ Bytes}$$
• Megabyte (MB): $$1 \text{ MB} = 1024 \text{ KB} = 2^{20} \text{ Bytes}$$
• Gigabyte (GB): $$1 \text{ GB} = 1024 \text{ MB} = 2^{30} \text{ Bytes}$$
• Terabyte (TB): $$1 \text{ TB} = 1024 \text{ GB} = 2^{40} \text{ Bytes}$$
• Petabyte (PB): $$1 \text{ PB} = 1024 \text{ TB} = 2^{50} \text{ Bytes}$$

Binary vs. Decimal Representation

It's important to distinguish between binary and decimal representations of data storage. Computers use binary (base-2), while we often use decimal (base-10) in everyday life. The prefixes (kilo, mega, etc.) have different meanings in binary and decimal.

For example, $$1 \text{ KB}$$ in decimal is approximately 1000 bytes, but in binary it's exactly 1024 bytes.

Table of Storage Units

The following table summarizes the relationship between these storage units:

Unit	Abbreviation	Decimal Equivalent (approximate)	Binary Equivalent
Bit	b	-	1
Byte	B	1024	8
Kilobyte	KB	1024	1024
Megabyte	MB	1024	1024
Gigabyte	GB	1024	1024
Terabyte	TB	1024	1024
Petabyte	PB	1024	1024

Calculating Storage Capacity

To calculate the total storage capacity of a device, you need to know the number of storage units it has. For example, a hard drive might be advertised as having 1 TB of storage. This means it can store 1,024,000,000,000 bytes of data.

Data Compression

Data compression is a technique used to reduce the amount of storage space required for data. This is achieved by removing redundancy in the data. There are two main types of compression:

• Lossless Compression: This method reduces file size without losing any data. The original data can be perfectly reconstructed from the compressed data. Examples include ZIP files and PNG images.
• Lossy Compression: This method reduces file size by discarding some data that is considered less important. The original data cannot be perfectly reconstructed. Examples include JPEG images and MP3 audio files.

Data compression is crucial for efficient data storage and transmission.