What is the binary number for 678?

Answer 1

The number 678 in binary is the ten-digit number 1010100110.

(10101 00110)

The digits in a binary number are exponents of 2 rather than 10, so that for a ten-digit number in binary, the digit places represent

512, 256, 128, 64, 32, 16, 8, 4, 2, 1 instead of increasing values of 10.

1010100110 = 512 + (0x256) + 128 + (0x64) + 32 + (0x16) + (0x8) + 4 + 2 + (0x1) = 678

This was determined using the subtraction method:

678 - 512 = 166 (1)

no 256 (0)

166 - 128 = 38 (1)

no 64 (0)

38 - 32 = 6 (1)

no 16 (0)

no 8 (0)

6 - 4 = 2 (1)

4 - 2 = 0 (1)

no 1 (0)

= 1010100110