IOTA Tutorial 2 | Trit and Tryte

IOTA Tutorial

Trit and Tryte

In this video series different topics will be explained which will help you to understand IOTA.
It is recommended to watch each video sequentially as I may refer to certain IOTA topics explained earlier.

The trinary numeral system has two types:
The balanced trinary system in which a trit has the values -1, 0 and 1.
The unbalanced trinary system in which a trit has the values 0, 1 and 2.
In this presentation I will only focus on the balanced trinary system.
Trit means Trinary Digit, analogous to bit and has the following values: -1, 0 and 1.
Tryte means Trinary Byte, analogous to byte.
A tryte consists of 3 trits.

1 byte = 2^8 = 256 combinations
1 tryte = 3 trits = 3^3 = 27 combinations
5 trits = 3^5 = 243 combinations
5 trits is NOT equal to 1 byte

Convert tryte -1, 1, 0 to integer:
-1 x 3^0 + 1 x 3^1 + 0 x 3^2 = 2
Convert tryte 1, -1, 1 to integer:
1 x 3^0 + -1 x 3^1 + 1 x 3^2 = 7

What is the maximum value a tryte can have (not the number of combinations)?
Answer: 13
If you thought 3^3 – 1 = 26 you are thinking in the binary system.
If you have 2 bits in a binary system, you have the following combinations:
00 = 0x2^1 + 0x2^0 = 0
01 = 0x2^1 + 1×2^0 = 1
10 = 1×2^1 + 0x2^0 = 2
11 = 1×2^1 + 1×2^0 = 3
Max value = 2^2 – 1

If you have 2 trits in a balanced trinary system, you have the following combinations:
0, 0 = 0x3^0 + 0x3^1 = 0
0, 1 = 0x3^0 + 1×3^1 = 3
0,-1 = 0x3^0 + -1×3^1 = -3
1, 0 = 1×3^0 + 0x3^1 = 1
1, 1 = 1×3^0 + 1×3^1 = 4
1,-1 = 1×3^0 + -1×3^1 = -2
-1, 0 = -1×3^0 + 0x3^1 = -1
-1, 1 = -1×3^0 + 1×3^1 = 2
-1,-1 = -1×3^0 + -1×3^1 = -4

The values in the trinary system are balanced around zero:
-4, -3, -2, -1, 0, 1, 2, 3, 4
Max value = (3^2 – 1) / 2

A tryte has 3 trits, so the maximum value will be (3^3 -1) / 2 = 13 and it has 3^3 = 27 combinations.
A tryte will have the following values: -13, -12, …-2, -1, 0, 1, 2,…12, 13
Convert the following two trytes -1, -1, -1, 1, 0, 0 to an integer:
-1 x 3^0 + -1 x 3^1 + -1 x 3^2 + 1 x 3^3 + 0 x 3^4 + 0 x 3^5
-13 + 27 = 14

IOTA uses the balanced trinary system
To make the trytes more human readable the IOTA development team created the tryte alphabet:
9ABCDEFGHIJKLMNOPQRSTUVWXYZ
The tryte alphabet consists of 26 letters of the latin alphabet plus the number 9.
The tryte alphabet has a total of 27 characters.
Because 1 tryte has 3^3 = 27 combinations, each tryte can be represented by a character in the tryte alphabet.

Tryte alphabet:
Tryte Dec Char
0, 0, 0 0 9
1, 0, 0 1 A
-1, 1, 0 2 B
0, 1, 0 3 C
1, 1, 0 4 D
-1,-1, 1 5 E
0,-1, 1 6 F
1,-1, 1 7 G
-1, 0, 1 8 H
0, 0, 1 9 I
1, 0, 1 10 J
-1, 1, 1 11 K
0, 1, 1 12 L
1, 1, 1 13 M
-1,-1,-1 -13 N
0,-1,-1 -12 O
1,-1,-1 -11 P
-1, 0,-1 -10 Q
0, 0,-1 -9 R
1, 0,-1 -8 S
-1, 1,-1 -7 T
0, 1,-1 -6 U
1, 1,-1 -5 V
-1,-1, 0 -4 W
0,-1, 0 -3 X
1,-1, 0 -2 Y
-1, 0, 0 -1 Z

IOTA seeds, addresses, hashes, etc are trytes which are represented by characters from the tryte alphabet.
For example the integer 14, converted into trytes: -1, -1, -1, 1, 0, 0
Convert the trytes using the tryte alphabet:
-1, -1, -1 = N
1, 0, 0 = A

Thus integer 14 converted into trytes: NA
The word “Zoo” converted into trytes looks like: ICCDCD
The ASCII value of Z = 90, converted to trytes: 0,0,1,0,1,0 = IC
The ASCII value of o = 111, converted to trytes: 0,1,0,1,1,0 = CD

An IOTA seed contains 81 characters which is the same as 81 trytes.
For example: C9RQFODNSAEOZVZKEYNVZDHYUJSA9QQRCUJVBJD9KHAKPTAKZSNNKLJHEFFVK9AWVDAUJRYYKHGWQIAWF
Each tryte has 27 combinations, which means an IOTA seed has:
27^81 = ~8.71 x 10^115 combinations
In comparison a Bitcoin random number has:
2^256 = ~1.15 x 10^77 combinations

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