How do you convert 240 to a binary number?

Answer 1

27 ≤ 240 < 28 so the binary version will consist of 7 + 1 = 8 digits.

Set the first digit as 1, and the remainder is 240 - 27 = 240 - 128 =112 26 ≤ 112 so the second digit is 1 and the remainder is 112 - 26 = 112 - 64 = 48

25 ≤ 48 so the third digit is 1 and the remainder is 48 - 25 = 48 - 32 = 16

24 = 16 so the fourth digit is 1 and the remainder is 16 - 24 = 16 - 16 = 0

Since the remainder is 0, the rest of the digits are 0.

Therefore 2402 = 11110000

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In Simpler Terms

To create a binary number, use places for all exponent values of 2 that are less than your number. Subtract the largest digit and see if each successive smaller digit can be subtracted. If it can, enter a 1 value and subtract again. When your remainder is zero, put a 0 in all the remaining digits to the right.

240 - 128 = 112 (1)

112 - 64 = 48 (1)

48 - 32 = 16 (1)

16 - 16 = 0 (1)

no 8 (0)

no 4 (0)

no 2 (0)

no 1 (0)

= 11110000

Check: 11110000 = 128+64+32+16+0+0+0+0 = 240