# Could a standardized ternary system be more efficient than the binary system? [duplicate]

Could a standardized ternary (base-3) system be more efficient than the binary (base-2) system? Binary is efficient for processing using logic gates, but can be bulky when using for file storage or file transfer. I am interested in the feasibility of a ternary system both for file storage, file transfer, and computational processing.

The following three examples show an ASCII word converted to both binary and ternary, along with the length of the sequence:

ASCII Example 1: Hello

Binary: 0100100001100101011011000110110001101111 (40 characters)

Ternary: 210011101002200222 (18 characters)

ASCII Example 2: Test

Binary: 01010100011001010111001101110100 (32 characters)

Ternary: 220200002020100202 (18 characters)

ASCII Example 3: Cat

Binary: 010000110110000101110100 (24 characters)

Ternary: 22022100102101 (14 characters)

As denoted by the character count, the length of the ternary sequence can sometimes be less than half the length of the binary sequence. Having shorter sequences would be beneficial for file transfer, file storage, and computational processing speeds. On the surface this seems preferable, but perhaps there are disadvantages or implementation flaws which I am overlooking. The following contains additional observations (which may or may not be feasible), for implementation.

File Storage

Ternary would be highly beneficial for file storage but would require hardware changes. For example, manufacturers of flash memory storage devices such as flash drives or solid state drives would have to re-architect the transistors in order to store the representation of a 0, 1, or 2. If these transistors could maintain the same size dimensions as the current transistors that store the representation of a 0 or 1, the storage capacity has the potential to double.

File Transfer (Focus on wireless transmission)

File transfer speeds appear to have potential to increase with a ternary system. In the case of wireless transmissions, binary is generally preferred over analog due to its increased ability to maintain information integrity and is easier to distinguish when interference is present. The following diagram demonstrates this principle.

I imagine the implementation of ternary in wireless systems to appear like the following diagram (drawn quickly), having the peak and trough like a binary signal along with an ‘in-between’ to represent a 2. Having an ‘in-between’ might make the signal become less interference-tolerant than binary, which could be a disadvantage.

Thanks in advance for responses. Feel free to address unconsidered factors of why ternary may or may not be feasible and/or a beneficial alternative to the binary system.

EDIT: This question was flagged as a possible duplicate question. Keep in mind that an important aspect of this question is file transmission, which has been unaddressed in previous related ternary questions.

## marked as duplicate by David Richerby, Evil, Yuval Filmus algorithms StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Apr 3 '18 at 11:09

• An important aspect of this question is file transmission, which has been unaddressed in previous related ternary questions. – JaceVoracek Apr 4 '18 at 13:15
• If that is the only aspect that has been unaddressed, then I suggest you either edit this question to only ask about that or ask another question about that specifically. Apart from a duplicate, the current question seems too broad. – Discrete lizard Apr 5 '18 at 8:21

Whether this is more efficient depends on the physical properties of the medium, not on any fundamental principle of computer science. And of course there's no reason to limit yourself to ternary systems; we can consider systems with $k$ levels, where $k$ is any integer with $k \ge 2$ (it doesn't have to be limited to $k=2$ or $k=3$).
For instance, Wifi apparently uses BSK (a binary system, $k=2$), QPSK (a quad-level system, $k=4$), 16-QAM (a 16-level system), or 64-QAM (a 64-level system). Cable TV apparently uses 64-QAM and 256-QAM, which is a modulation scheme that uses $k=64$ or $k=256$ different levels. Why? Because this is more efficient than using a binary ($k=2$) system. There are many other examples like this in the communications world.
On the other hand, digital circuits -- as typically used in a CPU -- seem to be most effective with two-level modulation (i.e., binary, $k=2$). Why? The physics are different.