Will there ever be a day when all QR codes are used up?

Author: Wang Rifang

Reviewer: Chen Xudong

With the development of network technology and the popularity of smart phones, QR codes are everywhere in our lives. Payment, ride, business card, health code... more and more scenes have QR codes. According to statistics, 10 billion QR codes are consumed every day in the world, and more than 3 trillion are consumed every year. Such a huge amount of usage makes people worry. Will there be a day when QR codes will be used up? How many QR codes are left for us to use? How long will the remaining QR codes last? Today, let's take you to understand the ubiquitous QR codes in our lives.

Will there be a day when QR codes will be used up? The answer is definitely yes. Due to the size limit of QR codes, the number of QR codes is limited, but it will take a long time to use them up. It will take about 10,000 years to use up all the QR codes. Why are QR codes so durable? Let's start with the principle of QR codes.

Two-dimensional bar code is a black and white graphic that records data symbol information in a certain geometric shape distributed in a plane (two-dimensional direction) according to a certain rule. In the code compilation, the concept of "0" and "1" bit streams that constitute the internal logic basis of the computer is cleverly used, and several geometric shapes corresponding to binary are used to represent text numerical information. It is automatically read by image input equipment or photoelectric scanning equipment to realize automatic information processing: it has some common features of bar code technology: each code system has its own specific character set; each character occupies a certain width; has a certain verification function, etc. At the same time, it also has the function of automatically identifying information in different rows and processing graphic rotation change points.

Since there are many ways to encode a QR code, there are actually many types of QR codes. The one we often come into contact with in our lives is actually called QR Code, which stands for Quick Response Code. Its main feature is ultra-high-speed recognition. It also has the advantages of large information capacity, high reliability, the ability to represent a variety of text information such as Chinese characters and images, and strong confidentiality and anti-counterfeiting.

There are 40 versions of QRCode. Version 1 has a specification of 21x21, which is a square pattern with 21 modules in each row and column. Each version has 4 more modules on each side than the previous version. Version 40 is a 177x177 matrix. Black represents 1 and white represents 0 in the matrix. Different information is expressed through different combinations of 0 and 1. In layman's terms, the total number of styles composed of all black and white arrangements of version 1 plus the total number of styles composed of all black and white arrangements of version 2... all the way up to version 40, this is the total number of QR codes.

Take a 2x2 matrix as an example. In this matrix, each small square can have two colors, black and white. One square has two possibilities, two squares have four possibilities, three squares have eight possibilities, and four squares have 16 possibilities. Therefore, such a 2×2 matrix can form 2^4, 2 to the fourth power, and a total of 16 graphics can be obtained.

There are some fixed areas in the QR code that are used for positioning and redundant error correction. After removing these blocks, we can get the total number of blocks carrying data. With this number, we can calculate the total number of styles in each version.

Now we can roughly calculate the total number of QR codes in version 1. After removing the fixed blocks, there are 208 blocks in version 1 that can carry data, so version 1 can have 2 to the power of 208 possibilities, 2^208 is approximately equal to 4.1137 × 10^62, which is 4 followed by 62 zeros. You may not have a good idea of ​​this number, but we can compare it in another way. The current global population is about 8 billion, and 2^33 is about 8.5 billion, so the total number of QR codes in version 1 is many times more than the global population.

The commonly used code specification for WeChat Pay is a 25×25 version 2 QR code. After removing the blocks for positioning and redundant error correction blocks, there are 478 blocks left, so 478 small blocks can theoretically form a total of 2^478 QR codes, which is almost the same as the total number of atoms in the universe to the power of 10^80. The "2020 Code-based Economic War Epidemic Report" stated that during the epidemic (from January 23, 2020 to May 6, 2020), the total number of codes used by government, enterprises and individuals reached 140 billion times. We assume that WeChat uses 600 billion QR codes per year, so the QR codes for WeChat Pay are enough for WeChat to use for 2^478/600 billion=1.301x10^132 years.

This is just the data calculated from two versions of the QR code. There are 38 more versions of the QR code, and the number of QR codes that can be generated is far greater than these two versions. So even if the number of QR codes is limited, for the volume we use now, the QR codes are also inexhaustible within our foreseeable range.

References:

[1] Xu Guohui, Chen Jiexian. Principles and applications of mobile phone QR code technology[J]. Information and Computer: Theoretical Edition, 2013(1):2.

[2] Tencent WeChat’s “2020 Economic “War Against Epidemic” Report on QR Codes” Basic Structure and Generation Principles

[3] Basic structure and generation principle of QR code, CSDN, November 27, 2016, https://blog.csdn.net/u012611878/article/details/53167009

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