Convert decimal numbers a) 998 b) 653 into binary

a) To obtain a decimal number in binary form, we sequentially divide it by two, each time writing the result as an integer and a remainder. Division must be continued until there is a number equal to one.

998/2 = 499 remainder 0

499/2 = 249 remainder 1

249/2 = 124 remainder 1

124/2 = 62 remainder 0

62/2 = 31 remainder 0

31/2 = 15 remainder 1

15/2 = 7 remainder 1

7/2 = 3 remainder 1

3/2 = 1 remainder 1

Successive division by two gives the following sequence of remainders: 011001111. Unfolding it in reverse, we get the required number: 1111100110.

b) similarly we find 653 (10) = 1010001101 (2)