How do you convert from base 10 to base 2 without division?

Answer 1

1. Write out the powers of 2 from 20 = 1 (in right to left order, ie ... 16 8 4 2 1) until you get a power greater than or equal to the number you wish to convert.

2. Put a one (1) under the highest power of 2 that is less than or equal to the number

3. Subtract that power from the number.

4. If the result of the subtraction is not zero, find the next power of 2 not greater than the result of the subtraction and repeat from step 3.

5. Put a zero (0) under all powers of 2 which have nothing under them.

6. The result (under the powers of 2) is the number in base 2.

Example to convert 948 base 10 to base 2:

Write out the powers of 2 until greater than or equal to 948:

Powers: 1024...512...256...128...64...32...16...8...4...2...1

First power less than or equal to 958 is 512:

Powers: 1024...512...256...128...64...32...16...8...4...2...1

Result:.....................1.......................................................................

948 - 512 = 436

Next power not greater than 436 is 256:

Powers: 1024...512...256...128...64...32...16...8...4...2...1

Result:.....................1........1..............................................................

436 - 256 = 180 → 128:

Powers: 1024...512...256...128...64...32...16...8...4...2...1

Result:.....................1........1.........1.................................................

180 - 128 = 52 → 32:

Powers: 1024...512...256...128...64...32...16...8...4...2...1

Result:.....................1........1.........1...............1...............................

52 - 32 = 20 → 16

Powers: 1024...512...256...128...64...32...16...8...4...2...1

Result:.....................1........1.........1...............1......1.......................

20 - 16 = 4 → 4:

Powers: 1024...512...256...128...64...32...16...8...4...2...1

Result:.....................1........1.........1..............1......1..........1...........

4 - 4 = 0, so fill in the zeros:

Powers: 1024...512...256...128...64...32...16...8...4...2...1

Result:.....................1........1.........1.......0.....1......1....0...1...0...0

Thus 95810 = 11 1011 01002

(If the powers are written out in ascending order (from left to right), reverse the final result.)