# Binary Number

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## Introduction: Binary Number

This instructable describes how to create a binary number. You will need a handful of coins, a method for ordering them based on their position on a flat surface, and a mapping from the set {heads tails} to the set {0 1}. You will also need a flat surface large enough to hold the coins (0.1 square meter or more), and a method for recording the sequence of discrete values resulting from the process.

## Step 1: Gather Coins Into Hands

Gather the coins into your hands. You may scoop them up, or use one hand to slide coins into the palm of your other hand. Either hand may perform the sliding task. If you like, you may ask your partner to help gather the coins and place them in your hands. Note that the number of coins you use will be limited by the volume capacity of your handhold. In order to leave extra room within the cavity of your cupped hand, you should only fill the volume partway. 10 to 20 percent fillrates are recommended. For a typical adult hand, 5-10 coins seems to be a good amount.

## Step 2: Enclose Coins With Hands

With your hands assuming a cupped configuration, palm toward palm, cover the coins with both hands. Ensure that a tight seal is maintained along the perimeter of the hand cavity.

## Step 3: Agitate Coins

Repeatedly agitate the coins by moving hands in a forward-and-back motion. You may experiment with additional inputs such as exhaling/blowing on your hands, or repeating an exhortation such as "come on, seven!" The process of agitating the coins randomizes their states and their order. You can think of the randomness as a kind of fluid flowing from your neuromotor system to the set of coin states. If your neuromotor system exhibits typical randomness, four or five agitations suffice to randomize the coin states.

## Step 4: Release Coins Onto Surface

Release the coins onto the flat surface. It is recommended that you execute the release step from a low height relative to the surface so that gravitational potential is not converted to excessive kinetic energy. However, the release height should be sufficient to ensure that the coins avoid "piling up" on one another when they have come to rest on the surface.

## Step 5: Order the Coins

Assign an ordering to the coins. The ordering can be from left to right. Or from right to left. The ordering method should be established prior to the coin drop in order to avoid introduction of bias to the results. The ordering creates a correspondence between the natural numbers and the coins on the surface, establishing the identity of coin1, coin2, coin3, .. and so forth.

## Step 6: Map Coin-state to Binary Digit

Determine, via visual inspection, whether each coin is in its "heads" state or its "tails" state. Apply the mapping (heads,0) (tails,1) to convert each coin-state into a binary digit. Alternatively, apply the mapping (heads,1) (tails,0) to assign the binary digit 1 to coins in the heads state and the binary digit 0 to coins in the tails state. Select the mapping prior to releasing the coins in order to avoid introducing bias in the results.

## Step 7: Record Your Binary Number

After applying the mapping to each coin-state in sequence, record the resulting binary digits. You can record the digits from left to right or from right to left. Determine the recording method prior to releasing the coins in order to avoid introducing bias in the results.

Examples: 011000 1101 10010011

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