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Overview

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

2018-11-23 23.30.22

The contraption consists of:

  1. 3x 7-segment displays
  2. 3x 7-segment displays controllers
  3. 3x Base 2 to Base 10 converters (Binary -> Hexadecimal)
  4. An error redstone lamp
  5. 8x levers (4 for each number as input) that give 30 different combinations in total
  6. 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:

2018-11-23 23.31.54
  1. 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)
  2. 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 = 15
In our case 1101 we add up like this:
1 1 0 1
2^3 2^2 0 2^0
8 + 4 + 0 + 1 = 13
As 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

Decimal2binary

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.