Figured out quick equation to convert 6 bit binary nums

I was working on my binary clock and realized I need a way to quickly convert binary 0-60 without going through the whole 1*2^3+1*2^1 + ...... or else it would make my clock pointless.

This formula works for any number from 0-63. I am certain there is another likewise simple equation for numbers with more bits, and maybe this topic will challenge you guys to determine it.

Say you have a 6 bit binary number ABCDEF where A is the MSB and F is the LSB.

To convert to base 10, you do the following.

((ABC in base 10)*8) +(DEF in base 10).

All it requires you to remember is binary numbers 0-7, and most people can already do that.

So okay, now figure out a formula for 8 bits. Go!!!!

That's octal to decimal... You can do the analogous thing with any base that's a power of 2 -- just group the bits appropriately.

Figured it out for 10 bit numbers also.

Say you have an 8 bit number ABCDEFGH

To convert to base 10, you do

((ABCD in base 10) *16) + (EFGH in base 10)

This requires you to know 0-15 in binary. That is pretty much all I memorized. Anything higher than 16, I gotta convert. LOL.

Just imagine you can convert any number from 0-255 in mere seconds, in your head!!!

To be honest this is only useful on exams where your professor does not allow calculators. At work you can use calculators, and even supercomputers. Whatever you want.

Lets do an example:

Convert the following binary number:

01100100

First: 0110 is 6.
Second: 16*6 = 96
Third: 0100 is 4.
Fourth: 96 +4 = 100

We check using a calculator, and indeed 01100100 = 100 in decimal.

someonesdad is right, this will work for any power of 2. The next one (10 bits) requires you to memorize 0-31 in binary. Little tougher, but if you can, you can convert any number from 0-1023 in your head in seconds!!!

A good computer algorithm is to divide by two, over and over. If the answer is not even it is a 1, if it is even it is a 0.

Start with a decimal number 273.

273/2=136.5 1
136/2=68.....0
68/2=34.......0
34/2=17.......0
17/2=8.5......1
8/2=4..........0
4/2=2..........0
2/2=1..........0

273 Decimal = 10001000 Binary

Something went wrong:
273 decimal = 100010001 binary

Markd77 said:

Something went wrong:
273 decimal = 100010001 binary

Click to expand...

Forgot the last step...

273/2=136.5 1
136/2=68.....0
68/2=34.......0
34/2=17.......0
17/2=8.5......1
8/2=4..........0
4/2=2..........0
2/2=1..........0
1/2=0.5.......1

273 Decimal = 100010001 Binary

The number is read backwards, least significant digit first.

OK, something simpler, Decimal 11

11/2=5.5 1
5/2=2.5 . 1
2/2=1 .... 0
1/2=0.5 . 1

1011

or Decimal 12
12/2=6 .0
6/2=3 . 0
3/2=1.5 1
1/2=0.5 1

1100