Binary in Commands

Introduction ​

Binary (Base-2) is a mathematical system that allows you to represent any integer using only two states: 0 (Off/False) and 1 (On/True).

While humans typically use Base-10 (0–9), computers use Binary to perform complex tasks. In a way, they can also be used in command systems like bulk item selling or coordinate detection—with significantly fewer commands than linear methods would require.

How Binary Works ​

In a binary system, each digit is called a bit. Each bit's position represents a specific power of 2, increasing from right to left.

Conversion Example ​

To convert the binary number 1101 to a standard number, you sum the values of the positions where a 1 is present:

• 1 in the 8s place (2^3)
• 1 in the 4s place (2^2)
• 0 in the 2s place (2^1)
• 1 in the 1s place (2^0)

8 + 4 + 0 + 1 = 13

Implementation in Bedrock Commands ​

The primary advantage of binary in commands is optimization. Instead of running 64 commands to check if a player has 1 to 64 items, you can use just 7 binary steps ($2^0$ through $2^6$).

Example: Binary Shop System ​

This system clears items from a player's inventory and rewards them with a scoreboard currency. By checking for the largest possible power of 2 first, the system "deconstructs" any stack size efficiently.

## Check For 64 (2^6)
execute as @a[hasitem={item=bread,quantity=64..}] run scoreboard players add @s wiki:money 64
execute as @a[hasitem={item=bread,quantity=64..}] run clear @s bread 0 64

## Check For 32 (2^5)
execute as @a[hasitem={item=bread,quantity=32..}] run scoreboard players add @s wiki:money 32
execute as @a[hasitem={item=bread,quantity=32..}] run clear @s bread 0 32

## Check For 16 (2^4)
execute as @a[hasitem={item=bread,quantity=16..}] run scoreboard players add @s wiki:money 16
execute as @a[hasitem={item=bread,quantity=16..}] run clear @s bread 0 16

## Check For 8 (2^3)
execute as @a[hasitem={item=bread,quantity=8..}] run scoreboard players add @s wiki:money 8
execute as @a[hasitem={item=bread,quantity=8..}] run clear @s bread 0 8

## Check For 4 (2^2)
execute as @a[hasitem={item=bread,quantity=4..}] run scoreboard players add @s wiki:money 4
execute as @a[hasitem={item=bread,quantity=4..}] run clear @s bread 0 4

## Check For 2 (2^1)
execute as @a[hasitem={item=bread,quantity=2..}] run scoreboard players add @s wiki:money 2
execute as @a[hasitem={item=bread,quantity=2..}] run clear @s bread 0 2

## Check For 1 (2^0)
execute as @a[hasitem={item=bread,quantity=1..}] run scoreboard players add @s wiki:money 1
execute as @a[hasitem={item=bread,quantity=1..}] run clear @s bread 0 1

Advanced Use Cases ​

Get Coordinate as Scores ​

Detecting a player's exact X, Y, or Z coordinate is performed using a Binary Search Tree. Instead of checking every possible coordinate, you use a series of execute commands to narrow down the player's position relative to a fixed point.

By checking if a player is within a volume of 32,768 blocks, then 16,384, and so on down to 1 block, you can pinpoint their exact position across the world in just 16 steps. This is the most performance-efficient way to convert spatial data into scoreboard integers for use in calculations or teleports.

Implementation With MEF ​

You can also incorporate a binary tree into Multiplicative Execution Forking (MEF) to create complex geometries, terrain, or custom generations, such as a village or backrooms, with a single command!