Converting numbers between Base’s

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The method I will be showing relies on whole numbers so when asked to divide remember no .5, .3 ect..... 15 divided by 2 is 7 remainder 1 and so on. The whole number is placed in the cell under the number divided so 7 would appear under 15 as 15 divided by 2 is 7 remainder 1 the remainder column stores the 1.

Decimal to Binary

Lets convert 240 into Binary which is base 2 with the digits 0 & 1 only:-

D2B.jpg

Now looking at the remainder column only we get :-

D2B2.jpg

Topple the tower right and we get :- 11110000 a nice Binary number that is equal to 240 Decimal.

Decimal to Hex

& Now to HEX which is Base 16 which has the digits 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

D2H.jpg

Now looking at the remainder column only we get :-

D2H2.jpg

The first thing you should see is the 15 is not a single digit but as HEX goes 0 to F as shown below the 15 is replaced by an F so when you topple the tower to the right you get F0 which is equal to 240 Decimal or 11110000 Binary.

D2H3.jpg

The top line is Decimal and the bottom line is HEX.

Decimal to Octal

Ok so HEX was not too bad how about Octal which is Base 8 with the digits 0,1,2,3,4,5,6,7 can this method work here too :-

D2O.jpg

Now looking at the remainder column only we get :-

D2O2.jpg

Topple the tower right and we get :- 360 which is 240 in Decimal, F0 in HEX and 11110000 in Binary so yes this method works again.

NOTE: All information contained within this article is pure opinion. Although this article is intended to help people, it may contain faulty or misleading information. This article is not to be considered professional opinion or advice, and is in no way a replacement for reading all safety/instructional documentation. Always remember to protect yourself when handling/using hazardous materials, as well as test new techniques before using them on projects/work intended to be handed in or used.

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