Computer Science

# Common Base Conversions

Source: https://www.tes.com/teaching-resource/0-9-digit-cards-6044974 |

**base 10 system**because it has ten digits. There are three other common bases that are studied in C.S.: base 2, 8 and 16, with two, eight and sixteen digits, respectively. Before we examine each of these in more detail, your are probably asking...

**Why do we need to learn manual base conversions?**

**Although humans read in base-10, computers read in base-2 as the internal mechanisms can only reliably provide two options (i.e. are switches) that make data storage only possible in binary. But as the number gets larger the characters of binary get much larger and unwieldy to work with when examining computer codes. In the past, base-8 was used to shorten these long strings of numbers into more manageable chunks, but today this base-16 has supplanted octal in this role because it is more efficient. Now, we will move onto how to convert between these systems. We will use "binary" as a base case from which you can access the other bases (i.e. you would not convert directly from decimal to octal, but from decimal to binary and then from binary to octal).**

**Binary and Decimal:**

**First we examine the question of how to convert between our native number system and binary.**

Source: https://www.geeksforgeeks.org/program-binary-decimal-conversion/ |

Source: https://brilliant.org/wiki/binary-coded-decimal-or-bcd/ |

Source: https://owlcation.com/stem/How-to-Convert-Decimal-to-Binary-and-Binary-to-Decimal |

**Binary and Octal:**

Source: https://www.wikihow.com/Convert-Binary-to-Octal-Number |

Another example of binary to octal: https://circuitglobe.com/octal-to-binary-and-binary-to-octal-conversion-methods.html |

Chart for the octal digits: https://www.youtube.com/watch?v=a4i1OnDtufc |

Octal to Binary: https://circuitglobe.com/octal-to-binary-and-binary-to-octal-conversion-methods.html |

**Binary and Hexadecimal:**

Source: https://owlcation.com/stem/How-to-Convert-Hex-to-Binary-and-Binary-to-Hexadecimal |

Extra Sources

https://www.researchgate.net/post/Why_do_we_need_various_number_base_conversions_number_system_conversions_eg_octal_to_hexadecimal2

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