Question

Convert decimal 298 to base 2, 8, and 16 using mathematics. Please show all work.

Answer 1

1)  base-2
Divide 298 successively by 2 until the quotient is 0
298/2 = 149, remainder is 0
149/2 = 74, remainder is 1
74/2 = 37, remainder is 0
37/2 = 18, remainder is 1
18/2 = 9, remainder is 0
9/2 = 4, remainder is 1
4/2 = 2, remainder is 0
2/2 = 1, remainder is 0
1/2 = 0, remainder is 1
Read remainders from the bottom to top as 100101010
Answer: 100101010

2)  base-8
Divide 298 successively by 8 until the quotient is 0
298/8 = 37, remainder is 2
37/8 = 4, remainder is 5
4/8 = 0, remainder is 4
Read remainders from the bottom to top as 452
Answer: 452

3)  base-16
Divide 298 successively by 16 until the quotient is 0
298/16 = 18, remainder is 10
18/16 = 1, remainder is 2
1/16 = 0, remainder is 1
Read remainders from the bottom to top as 12A
Answer: 12A