Converting numbers between Base’s

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:-

Now looking at the remainder column only we get :-

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

Now looking at the remainder column only we get :-

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.

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 :-

Now looking at the remainder column only we get :-

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.