Question
2. Perform the following base conversions using subtraction or division-remainder:
a) 588 base10 = _________ 3
b) 2254 base10 = ________ 5
c) 652 base10 = ________ 7
d) 3104 base10 = ________ 9
Answer
a)
To convert the number given in base 10 to base 3, we need to divide the given number with 3 recursively till the remainder is 0. First we divide 588 with 3. The quotient is 196, remainder is 3. The remainder 3 will be the Least Significant Bit (last digit) in the required number in base 3. Now divide 196 with 3 again. Similarly proceed till the remainder is 0. The required number in base 3 can be obtainded by arranging remainder in each step from right to left. The following table illustrates the dividents (quotients) and remainders in each step.
|
Divisor |
Dividend |
Reminder |
|
3 |
588 |
|
|
3 |
196 |
0(LSB) |
|
3 |
65 |
1 |
|
3 |
21 |
2 |
|
3 |
7 |
0 |
|
|
2(MSB) |
1 |
(588)10 = (210210)3
b)
|
Divisor |
Dividend |
Reminder |
|
5 |
2254 |
|
|
5 |
450 |
4(LSB) |
|
5 |
90 |
0 |
|
5 |
18 |
0 |
|
3(MSB) |
3 |
(2554)10 = (33004)5
c)
|
Divisor |
Dividend |
Reminder |
|
7 |
652 |
|
|
7 |
93 |
1(LSB) |
|
7 |
13 |
2 |
|
1(MSB) |
6 |
(652)10 = (1621)7
d)
|
Divisor |
Dividend |
Reminder |
|
9 |
3104 |
|
|
9 |
344 |
8(LSB) |
|
9 |
38 |
2 |
|
4(MSB) |
2 |
(3104)10 = (4228)9