## Overview

The contraption was initiated by xSlendiX on 22/11/2018 and later finished on 23/11/2018.

The contraption consists of:

- 3x 7-segment displays
- 3x 7-segment displays controllers
- 3x Base 2 to Base 10 converters (Binary -> Hexadecimal)
- An error redstone lamp
- 8x levers (4 for each number as input) that give 30 different combinations in total
- A 4-bit full binary adder (4 inputs, 5 outputs because 15+15=30 and the max on display is 15)

## How it works

First, we give number 1 and number 2 inputs. The input is then fed into two different parts for each of the numbers:

- The Base 2 to Base 10 converters -> This allows us to see a preview in hexadecimal all the way up to 15 (2-3 ticks)
- A 4-bit full binary adder -> This is where the complicated boolean logic is working

After it calculates (4-5 ticks), the output is then fed into another Base 2 to Base 10 converter (for seeing the output) and it usually takes 2-3 ticks to output the number.

## Binary

### Converting binary number to decimal value

If we had for example a number for example 1101, we need to add up the powers of two then needed:

1 1 1 1

2^3 2^2 2^1 2^0

8 + 4 + 2 + 1 = 15In our case 1101 we add up like this:

1 1 0 1

2^3 2^2 0 2^0

8 + 4 + 0 + 1 = 13As we can see, we exclude the numbers that have the value of 0, we only keep the ones with value of 1.

### Converting decimal value into binary

Let's say we have the number 17. How do we convert it into binary?

First, we turn our number into primitive factors but with a small change, we only divide the number with 2 and put the remains next to the 2 like in the image below, finally, when you are done, you need to put a 1 at the end, after that, we read the numbers from down to up in our case it is 10001.