How do you change decimals to binary?

Answer 1

Binary to decimal is actually very simple.

Here is a "Base 10" (Decimal) number 7.

Binary is logically laid out in groups of 4 like:

0000 0000 0000 0111

It is read Right to Left and each 0/1 has a "Place Value". Starting at the right and moving left you have (1,2,4,8) (16,32,64,128) (256,512,1024,2048) (4096,8192,16384,32768).

Now, every where that there is a ONE you take its "Place Value" and add all of them up.

So, in our example we have 0111

i.e. (1 + 2 + 4 = 7)

Answer 2

By performing a base conversion. There are several algorithms for doing this.

The most commonly used manual algorithm for base conversions is a variant of long division.

Or you can do it on a converting calculator in a single keystroke.

To convert a decimal number to any other base (using long division):

1. Divide the number by the new base to get a [whole number] quotient and a remainder
2. note the remainder
3. replace the number by the quotient
4. if the number is not zero repeat from step 1
5. write the remainders out in reverse order: this is the decimal number in the new base.

eg to convert decimal number 233 to binary (base 2):

233 ÷2 = 116 r 1

116 ÷ 2 = 58 r 0

58 ÷ 2 = 29 r 0

29 ÷ 2 = 14 r 1

14 ÷ 2 = 7 r 0

7 ÷ 2 = 3 r 1

3 ÷ 2 = 1 r 1

1 ÷ 2 = 0 r 1

→ 23310 = 111010012

eg to convert decimal 233 to octal (base 8):

233 ÷ 8 = 29 r 1

29 ÷ 8 = 3 r 5

3 ÷ 8 = 0 r 3

→ 23310 = 3518