Zahlen, bitte! 65,536 – The frequently used limit number in IT

What connects Whatsapp, the CD, the Commodore 64, the high-color mode with older versions of Excel? Answer: the number 65536 as a limit. Due to its significance for the binary system, we come across the number again and again in IT. It also has some other exciting properties.

Mathematically, it is quite versatile. In binary,²¹⁶ equals 65,536 – that is the number of all possible bit combinations in 2 bytes. The binary number of 65,536 is 10000000000000000. It is not a prime number, as it has 17 divisors (1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4,096, 8,192, 16,384, 32,768, 65,536), some of which may be familiar to long-established IT experts. It is the smallest number with 17 divisors.

Furthermore, it is also the largest known power of two that does not contain the digits 1, 2, 4 or 8. It is also the sixth super perfect number: a number is considered super perfect if the sum of the divisors of the sum of its divisors is twice as large as the original number. And it has a famous neighbor: 65537, the fifth and largest Fermat number.

An important number in the binary system

But what does the number 65,536 mean in IT? Especially in the pioneering days, when memory space was still a precious commodity, the number achieved a certain fame, as 65,536 different values can be represented in a number of 16 binary digits (or bits). In programming, the number is referred to as an unsigned short integer.

In 8-bit systems such as the Commodore 64, 64 kilobytes or 65,536 bytes of memory were common. So why was it called C64? This is due to the property of the binary system, in which 1024 bytes make one kilobyte. 1,024 × 64 results in 65,536 bytes – however, the C65 was not a C64 calculated in the decimal system, as the mischievous now might think.

The SID (Sound Interface Device) was the pioneering sound chip on the C64. It was regarded as an electronic music synthesizer that offered 3 voices that could generate sounds in a frequency spectrum of 0 to 8.2 kilohertz in 65,536 steps per channel.

A 16-bit microprocessor such as the Motorola 68000 or the i86 architecture can directly process 65,536 memory addresses or 2 bytes simultaneously. 16 bits stands for the word size (the amount of data that a computer processor can process in one step) of 65,536 bits.

16-bit color depth as an intermediate step

In color management, the number 65,536 is immortalized as 16-bit color depth: High-Color or XGA mode (Extended Graphic Adapter) was an intermediate step between SVGA (265 colors) and True Color (16.7 million colors). This allowed a palette of 65536 color values per channel (red, green, or blue) per pixel.

When we talk about CD quality today, there are two key figures: 44.1 kilohertz at 16 bits, which dates back to the days when the CD came onto the market and made sensational sound quality possible at the time. The 44.1 kilohertz stands for the sampling frequency, 16 bits refer to the sampling depth, which is listed in gradations from 0 to 65,536. The higher the value, the louder the recording.

The first 65,536 character codes in the Unicode character set represent the Basic Multilingual Plane (BMP). This contains the most commonly used characters across languages and countries. At Microsoft, 65536 set the tone for a long time: The number of rows was the maximum limit for tables that could be edited in Excel 2003 and older. Later versions already support 1048576 rows.

There are countless other examples of the 65536 limit, although they have become increasingly obsolete with technological progress and thanks to higher bandwidths and storage space. However, frequent smartphone writers still have to get used to it today, albeit at a high level: Whatsapp's character limit for a message is 65,536 characters. And you have to type for a long time to reach that.

(mawi)