Recently I started learning for BCS cert level and I was supposed to learn converting octals and hexadecimals to binary again after O/Ls. By then I was seeking some easy way to do this up as I’m not good and tricky at maths as you guys do. 🙂 My attempt here is to help out someone who stuck or wanted to save more time on exams by stopping calculations over and over. So this will just need a kindergarten skill: of remembering/fixing patterns.

Hey kiddos! Stay calm and learn.

It may no need of describing about these numeric systems much, but I hope some small one would make the stuff perfect.

Numbers we use come with a base. The common number system 0-9 goes with base 10 which named as Decimals. Literally computers aren’t Brainy as us so it’s Binary, base 2 including 0 (zero) and 1 (one). It also reduces the space of memory and increases the speed of calculations. (No, I don’t think you’d use in daily life btw 😉 ) Octal numbers, or oct for short, is the base 8 number system, and uses the digits 0 to 7. And then Hexadecimal is base 16 including 0 and 9 then A-F which some of you may know with CSS color codes. Beginners should remember that every last number of the system minus one to name. Decimal: 9, Oct 7 and so on because the Zero counts in.

Learning about these is so fun but as a professional web developer, I’ve never met to write anything in binary myself but only color codes in CSS. 😛 All these come besides the revolution of computer & computer languages, and these systems are its base. So computers worth learning from the Human teachers to help you aliens out.

Let’s get in to the methods. First,

## Octal to Binary

Here’s the table to convert Octal to Binary. With this you can easily replace given octal with corresponding binary. You may seen this before or your teacher asked this to be remembered for easy use. I know what you maths folks say: *How on earth we can remember these Eggs and Forks*? 😀 So here I ain’t asking you to remember this, but to build this up yourself at exam.

Oct | Bin |
---|---|

0 | 000 |

1 | 001 |

2 | 010 |

3 | 011 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

In a free advice, I should tell you that if you’re stuck at anything, just stand up and go away out of the earth and look at it. You’ll find how much smaller is that. Have a closer look at the line-up of binary column if you hadn’t before at classes. Wait! tell me you can’t or I’ll have to stop writing this post now. 😉

- I need you to look at the last (3rd) column of Binaries from left for the first pattern. There it goes like Zero-One, Zero-One; the way binary goes. The name of it, “binary” is the easiest way to remember the pattern there.
- Now find the 2nd or middle column of Binaries. It stays like Zero-Zero-One-One. Remember it like a song or think from itself, the first power of 2 (2
^{1}) is 2. So two Ones and two Zeros. - And 1st column of Binaries, Zero-Zero-Zero-Zero-One-One-One-One. Second power of 2 (2
^{2}) is 4. Then four Zeros – four Ones. Or just fill out half of table from the starting number.

You’re Welcome! 🙂 If you’re developing this on a paper, start Oct 0 to Bin 000. Keep space and write Oct 7 to Bin 111. It’ll make you easier and reliable to play with the pattern.

## Hexadecimal to Binary

The base 16 to base 2. Well, I can’t be the only one who heard convert 16 to 10, and then to base 2. Oh man WTHex! 😛 Say hello to the table of Binaries for Hexas, and my rotten pattern.

Hex | Bin |
---|---|

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

A | 1010 |

B | 1011 |

C | 1100 |

D | 1101 |

E | 1110 |

F | 1111 |

I know you got that, but wait. Last row geniuses in the class may not.

- Again first three columns of Binaries from left goes like the same I described above. 0-1, 00-11, 0000-1111.
- And the last new fourth column is also just third power of 2 (2
^{3}) is 8. Or half of table fills with starting point. Eight 0s and Eight 1s.

Hope any of you found this is useful and I even saved the time of figuring this out. Is there anymore methods you know for this? Or any for other ones like Logic Gates etc? Share it with me!