What is 345.125 in binary?

Answer 1

The method you must use to get to your answer is like this:

Perform a modulo operation of 2 on the number, write the digit down and perform an integer division of 2 on your number.

Then, repeat every step by writing the result of the modulo before your other modulo-digits. Your last number after the integer division will be a 1; write that number down as a digit before your modulo-digits. The number that consists of 0's en 1's is your decimal number in binary.

For example with the decimal number 345125:

345125%2=1

(345125)dec = (..1)bin

345125/2=172562

172562%2=0

(345125)dec = (..01)bin

172562/2=86281

86281%2=1

(345125)dec = (..101)bin

86281/2=43140

43140%2=0

(345125)dec = (..0101)bin

43140/2=21570

21570%2=0

(345125)dec = (..00101)bin

21570/2=10785

10785%2=1

(345125)dec = (..100101)bin

10785/2=5392

5392%2=0

(345125)dec = (..0100101)bin

5392/2=2696

2696%2=0

(345125)dec = (..00100101)bin

2696/2=1348

1348%2=0

(345125)dec = (..000100101)bin

1348/2=674

674%2=0

(345125)dec = (..0000100101)bin

674/2=337

337%2=1

(345125)dec = (..10000100101)bin

337/2=168

168%2=0

(345125)dec = (..010000100101)bin

168/2=84

84%2=0

(345125)dec = (..0010000100101)bin

84/2=42

42%2=0

(345125)dec = (..00010000100101)bin

42/2=21

21%2=1

(345125)dec = (..100010000100101)bin

21/2=10

10%2=0

(345125)dec = (..0100010000100101)bin

10/2=5

5%2=1

(345125)dec = (..10100010000100101)bin

5/2=2

2%2=0

(345125)dec = (..010100010000100101)bin

2/2=1

(345125)dec = (10100010000100101)bin

So the decimal number 345125 in binary is 10100010000100101.