Topics from the Cambridge IGCSE (9-1) Computer Science syllabus.

1.3.1 | DATA STORAGE MEASUREMENTS

Topics from the Cambridge IGCSE (9-1) Computer Science 0984 syllabus 2023 - 2025.

OBJECTIVES
1.3.1 Understand how data storage is measured

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TERMINOLOGY
QUESTIONS
FLASHCARDS
WORKBOOK

we’re going to dive into three ways to represent positive and negative numbers in binary: Sign and Magnitude, One’s Complement, and Two’s Complement. Let’s break down each method and see how they work. Part 1: Sign and Magnitude Let’s start with Sign and Magnitude. This is one of the simplest ways to represent positive and negative numbers in binary. Here’s how it works: In Sign and Magnitude, we use the leftmost bit – known as the sign bit – to indicate whether the number is positive or negative: If the sign bit is 0, the number is positive. If the sign bit is 1, the number is negative. The remaining bits represent the actual value, or magnitude. For example: In an 8-bit system, the binary number 0000 1010 has a sign bit of 0, meaning it’s positive. The remaining bits, 0000 1010, represent the number 10 in decimal. Now, if we change that sign bit to 1, making it 1000 1010, the number becomes -10 in decimal. The rest of the bits stay the same, representing the value. However, Sign and Magnitude has limitations because it can make binary arithmetic more complex, especially when dealing with subtraction. Part 2: One’s Complement Next, we have One’s Complement. This method also uses the leftmost bit as a sign bit, but it represents negative numbers differently. Here’s the rule for One’s Complement: To find the One’s Complement of a binary number, invert all the bits – that means changing 0s to 1s and 1s to 0s. For example: If we want to represent -10 in an 8-bit system: Start with the positive binary representation of 10, which is 0000 1010. Invert each bit to get the One’s Complement: 1111 0101. So, 1111 0101 represents -10 in One’s Complement. One’s Complement simplifies some operations, but there’s a problem: it has two representations of zero. 0000 0000 represents positive zero, and 1111 1111 represents negative zero, which can make arithmetic operations tricky. Part 3: Two’s Complement Finally, let’s look at Two’s Complement. This is the most widely used method because it solves the issue of having two zeros and makes binary arithmetic easier. Here’s how to find the Two’s Complement of a number: Start with the positive version of the number in binary. Invert all the bits to get the One’s Complement. Add 1 to the result. For example: Let’s represent -10 in Two’s Complement. Start with the positive version of 10 in binary: 0000 1010. Invert all the bits to get 1111 0101. Add 1 to the inverted result: 1111 0101 + 1 = 1111 0110. So, 1111 0110 represents -10 in Two’s Complement. Two’s Complement only has one representation of zero, which is 0000 0000. It also makes addition and subtraction much simpler for computers because they can treat both positive and negative numbers the same way during calculations. Part 4: Summary To recap: Sign and Magnitude uses a sign bit to indicate positive or negative, but it can make arithmetic tricky. One’s Complement inverts all the bits to represent negative numbers, but it has two zeros. Two’s Complement inverts all the bits and adds 1, making binary arithmetic easier and solving the two-zero issue. And that’s it! These three methods – Sign and Magnitude, One’s Complement, and Two’s Complement – are fundamental to understanding how computers represent both positive and negative numbers in binary. Thanks for listening, and I hope this explanation helps you see how each method works!

Read Aloud

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DATA STORAGE MEASUREMENTS

Data storage is measured in units of bytes, with larger units being used to represent larger storage capacities. For example, early computers such as the IBM 650 in the 1950s had a storage capacity of around 2000 characters, or roughly 2 kilobytes (KB) of data. By the 1980s, personal computers such as the Apple II and Commodore 64 had storage capacities of around 64 KB to 128 KB.

Today, modern computer storage devices such as hard disk drives, solid state drives, and USB flash drives have storage capacities that range from a few gigabytes (GB) to multiple terabytes (TB). For example, a typical laptop hard drive might have a capacity of 500 GB, while high-end solid state drives can have capacities of up to 4 TB.

Storage capacity can be represented in different formats, such as megabytes (MB), gigabytes (GB), terabytes (TB), and so on. However, these units are based on powers of 10, which can lead to confusion when dealing with binary data storage. To address this issue, a binary prefix system was introduced, which uses prefixes such as kibi-, mebi-, gibi-, and tebi- to represent binary multiples of bytes (powers of 2). For example, a kibibyte (KiB) represents 1024 bytes, while a megabyte (MB) represents 1000 bytes.

In summary, data storage is measured in units of bytes, with larger units being used to represent larger storage capacities. Early computers had relatively small storage capacities, while modern computer storage devices can store terabytes of data. Storage capacity can be represented in different formats, and binary prefixes such as kibi- and mebi- are used to represent binary multiples of bytes.

The following data storage notations are listed in order of size and an example use for each is given:

Bit: 1 bit represents a single binary digit, which can be either a 0 or a 1. Bits are used to represent the smallest unit of digital data and are often used in communication protocols and encryption algorithms.
Nibble: A nibble represents 4 bits of data, or half a byte. Nibbles are not commonly used in modern computing, but were used in older systems to represent hexadecimal values.
Byte: A byte represents 8 bits of data and is the basic unit of storage in most computer systems. Bytes are used to represent individual characters, such as letters and numbers, as well as larger data types such as images and audio.
Kibibyte (KiB): 1 KiB represents 1024 bytes of data. KiB is used to represent small to medium-sized files, such as text documents or low-resolution images.
Mebibyte (MiB): 1 MiB represents 1024 KiB, or 1,048,576 bytes of data. MiB is used to represent larger files, such as high-resolution images or short audio clips.
Gibibyte (GiB): 1 GiB represents 1024 MiB, or 1,073,741,824 bytes of data. GiB is used to represent even larger files, such as videos or large software applications.
Tebibyte (TiB): 1 TiB represents 1024 GiB, or 1,099,511,627,776 bytes of data. TiB is used to represent very large files, such as high-resolution videos or large databases.
Pebibyte (PiB): 1 PiB represents 1024 TiB, or 1,125,899,906,842,624 bytes of data. PiB is used to represent data storage at the petabyte level, such as in large data centers or cloud storage services.
Exbibyte (EiB): 1 EiB represents 1024 PiB, or 1,152,921,504,606,846,976 bytes of data. EiB is used to represent data storage at the exabyte level, such as in scientific research or big data applications.

CHECK YOUR KNOWLEDGE

Which of the following is the correct order of data storage units from smallest to largest?

A) Bit, Byte, Kilobyte, Gigabyte, Megabyte

B) Bit, Byte, Kilobyte, Megabyte, Gigabyte

C) Byte, Bit, Megabyte, Kilobyte, Gigabyte

D) Byte, Bit, Kilobyte, Terabyte, Megabyte

EXPLAINATION

The correct answer is B: "Bit, Byte, Kilobyte, Megabyte, Gigabyte." This follows the standard data measurement hierarchy, where each unit is a multiple of the previous unit (e.g., 1 Byte = 8 Bits, 1 Kilobyte = 1,024 Bytes).

Bit: 1 bit represents a single binary digit, which can be either a 0 or a 1. Bits are used to represent the smallest unit of digital data and are often used in communication protocols and encryption algorithms.
Nibble: A nibble represents 4 bits of data, or half a byte. Nibbles are not commonly used in modern computing, but were used in older systems to represent hexadecimal values.
Byte: A byte represents 8 bits of data and is the basic unit of storage in most computer systems. Bytes are used to represent individual characters, such as letters and numbers, as well as larger data types such as images and audio.
Kibibyte (KiB): 1 KiB represents 1024 bytes of data. KiB is used to represent small to medium-sized files, such as text documents or low-resolution images.
Mebibyte (MiB): 1 MiB represents 1024 KiB, or 1,048,576 bytes of data. MiB is used to represent larger files, such as high-resolution images or short audio clips.
Gibibyte (GiB): 1 GiB represents 1024 MiB, or 1,073,741,824 bytes of data. GiB is used to represent even larger files, such as videos or large software applications.
Tebibyte (TiB): 1 TiB represents 1024 GiB, or 1,099,511,627,776 bytes of data. TiB is used to represent very large files, such as high-resolution videos or large databases.
Pebibyte (PiB): 1 PiB represents 1024 TiB, or 1,125,899,906,842,624 bytes of data. PiB is used to represent data storage at the petabyte level, such as in large data centers or cloud storage services.
Exbibyte (EiB): 1 EiB represents 1024 PiB, or 1,152,921,504,606,846,976 bytes of data. EiB is used to represent data storage at the exabyte level, such as in scientific research or big data applications.

1: What is the size of a byte in bits?
a) 4 bits
b) 8 bits
c) 16 bits
d) 32 bits

2: Which of the following is a larger unit of storage than a gigabyte?
a) Megabyte
b) Terabyte
c) Kilobyte
d) Petabyte

3: How many bytes are in a mebibyte (MiB)?
a) 1024 bytes
b) 1000 bytes
c) 1,048,576 bytes
d) 1,000,000 bytes

4: What is the next largest storage unit after a tebibyte (TiB)?
a) Zebibyte (ZiB)
b) Pexabyte (PeB)
c) Exbibyte (EiB)
d) Yobibyte (YiB)

5: How many bits are in a nibble?
a) 1 bit
b) 2 bits
c) 4 bits
d) 8 bits