# 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, โฆ-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 โZooโ 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