32



|16 |8 |4 |2 |1 |Equation |Decimal |

|0 |0 |

|32 |0 |

|16 |0 |

|8 |1 |

|4 |1 |

|2 |1 |

|1 |0 |

|16 |1 |

|8 |0 |

|4 |1 |

|2 |1 |

|1 |1 |

So, 78 looks like 1001110 in binary code.

Here is another example which converts 23 into binary code:

23-16=7 7-4=3 3-2=1 1-1=0

The decimal number 23 is converted to 10111 in binary code.

The following table of binary digit values from the digits zero to ten may be useful to have or memorize.

|Digit: |10 |9 |8 |7 |

|F |61440 |3840 |240 |15 |

|E |57344 |3584 |224 |14 |

|D |53248 |3328 |208 |13 |

|C |49152 |3072 |192 |12 |

|B |45056 |2816 |176 |11 |

|A |40960 |2560 |160 |10 |

|9 |36864 |2304 |144 |9 |

|8 |32768 |2048 |128 |8 |

|7 |28672 |1792 |112 |7 |

|6 |24576 |1536 |96 |6 |

|5 |20480 |1280 |80 |5 |

|4 |16384 |1024 |64 |4 |

|3 |12288 |768 |48 |3 |

|2 |8192 |512 |32 |2 |

|1 |4096 |256 |16 |1 |

|0 |0 |0 |0 |0 |

Why do electrical systems communicate with binary code instead of decimal code? The reason is that binary code is more accurately interpreted than a counting system with more than two characters per digit, since each character is represented by a certain amount of voltage. Voltage acts a little like nature; it not always 100% precise (accurate) and seems to have a slight random or unpredictable aspect. So, in order to interpret the voltage’s representation we use a range that the voltage could be for each representation. The character zero is represented by a low voltage. The character one is represented by a high voltage. The graph shows an example of how voltage can be converted to binary code. If the voltage crosses the red line, the number represented is one. The binary number represented is 111010, which in decimal form is 58.

(I should change the diagram to square waves.)

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