Question

Convert the following decimal numbers to base 18 using the symbols you suggested in exercise 35. a. 1066, b. 99099, c. 1.

Answer 1

c.1

To convert decimal numbers to base 18, divide the decimal number by 18 and keep track of the remainders. Read the remainders, from right to left, to form the base 18 representation.

Step-by-step explanation:

To convert decimal numbers to base 18, we can divide the decimal number by 18 and keep track of the remainders. The remainder, when converted to the appropriate symbol, will be the rightmost digit in the base 18 representation. We continue dividing the quotient by 18 until the quotient becomes 0. The remainders, read from right to left, will form the base 18 representation of the decimal number.

a. 1066:

1066 ÷ 18 = 59 remainder 14 (E)

59 ÷ 18 = 3 remainder 5 (5)

3 ÷ 18 = 0 remainder 3 (3)

So, the base 18 representation of 1066 is 35E3.

b. 99099:

99099 ÷ 18 = 5505 remainder 9 (9)

5505 ÷ 18 = 305 remainder 15 (F)

305 ÷ 18 = 16 remainder 17 (H)

16 ÷ 18 = 0 remainder 16 (G)

So, the base 18 representation of 99099 is G17F9.

c. 1:

1 ÷ 18 = 0 remainder 1 (1)

So, the base 18 representation of 1 is 1.