Explore the Binary System Fundamentals – the Bits and Bytes

Introduction

Bits and bytes are the fundamental components that form the basis of the binary system. This system is used in most of computing applications in our world! From your calculator, laptop, to rocket and space communication. You may have heard of the term quantum computing, which aims to go beyond the limitation of binary system… Well…that is for the future, let’s take a look at the binary system that builds the world we know today.

Bits and Bytes

• A bit is the smallest unit of data in computing, representing a binary digit that can be either a 0 or a 1 (2 possible states, therefore the name binary system).
• A byte, on the other hand, is a group of 8 bits.

For example:

• 1 bit has 2 possible combinations: 0 or 1.
• 2 bits have 4 possible combinations: 00, 01, 10, 11.
• 3 bits have 8 possible combinations: 000, 001, 010, 011, 100, 101, 110, 111.
• 1 byte has 8 bits, which have 256 possible combinations: 00000000, 00000001, 00000010 … etc.
• 2 bytes have 16 bits, which have 65535 possible combinations.

Different Units of Measurements in Binary System

Like the metric system, binary system also uses international System of Units (SI) to represent a bit or byte value in different magnitudes: kilo, mega, giga, tera are quite common. Depending on the application, we use different units to measure different things:

Data Storage

We normally use byte to represent data storage size. For example, a file’s size or USB drive’s capacity are often represented in number of bytes.

• 1KB (kilobyte) => 1024 bytes
• 1MB (Megabyte) => 1024 kilobytes
• 1GB (Gigabyte) => 1024 megabytes
• 1TB (Terabyte) => 1024 gigabytes

Transfer Speed

We use byte per second to represent data transfer speeds. For example, when you copy a large file from your Windows 10 to a USB drive, a window will pop up to show you the speeds in byte per second and how many seconds left.

• 1 KB/s (Kilobyte per second) => 1024 bytes /s
• 1 MB/s (Megabyte per second) => 1024 kilobytes / s
• 1 GB/s (Gigabyte per second) => 1024 Megabyte / s

Network Throughput

We normally use bits per second to represent throughput. For example, when you are shopping for home internet, your speed option is often represented in bits per second.

• 1Kbps (Kilobit per second) => 1024 bits / s
• 1Mbps (Megabit per second) => 1024 kilobits / s
• 1Gbps (Gigabit per second) => 1024 megabits / s

Decimal and Binary System

Why is 1 kilo equals to 1024 but not 1000? The answer is “it depends”.

In the real world, our numbering system bases on the international system of units, which uses the decimal number system (base 10), which means:

• 1K: 1000
• 1M: 1000K
• 1G: 1000M

Computers, on the other hand, use the binary system (base 2), which means:

• 1K: 1024
• 1M: 1024K
• 1G: 1024M

The Missing GBs in my USB Drive?

Knowing the difference between the binary and the decimal system, can you tell me where my missing GBs of data go? I purchased a new hard drive rated at 1TB, connected to my computer, but it only shows 952 GB instead of 1 TB.

In fact, there is no missing GBs in my new hard drive. It is just the difference in data representation:

• I purchased a 1 TB hard drive measured in the decimal system, which equals 1000 GBs,
• I connected this hard drive to my computer.
• My computer uses the binary system, so it recognized 1 TB (in decimal) as 952 GB (in binary)
• There is no missing GBs, I received exactly 1000 GBs (in decimal) or 952 GBs (in binary), both representing the same number.

Summary

Bits and bytes are the basic building blocks of our computer system and are extremely important concept in C programming. Every variable, function, data type occupies different sizes of bytes in memory and C programming forces you to be aware of the bits and bytes that you are working with.

Related Posts

• A Closer Look at C Data Types and Variables