Question 1192171: Name: MAT 145: Topics In Contemporary Math
Bases
Covert each of the following decimal numbers into the required bases.
6) 957, base 2
7) 576, base 2
8) 65, base 3
9) 5000, base 7
10) 900, base 6
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! Covert each of the following decimal numbers into the required bases.
6) 957, base 2
Decimal to base 2 calculation:
Divide by the base to get the digits from the remainders:
Division........ Quotient........ Remainder(Digit)........ Digit #
957/2 .............478........................1..........................0
478/2 ..............239..................0........................ 1
239/2....................119.................1........................ 2
119/2.....................59....................1........................ 3
59/2.......................29.....................1........................ 4
29/2.....................14.....................1........................ 5
14/2........................ 7.......................0........................ 6
7/2........................ 3.......................1........................ 7
3/2........................ 1.......................1........................ 8
1/2........................ 0.......................1........................ 9
= (1110111101)2
7) 576, base 2
Division........ Quotient........ Remainder(Digit)........ Digit #
576/2....................288........................ 0........................ 0
288/2....................144........................ 0........................ 1
144/2...................72........................ 0........................ 2
72/2.....................36........................ 0........................ 3
36/2.....................18........................ 0........................4
18/2.....................9........................ 0........................ 5
9/2........................ 4........................ 1........................ 6
4/2........................ 2........................ 0........................ 7
2/2........................ 1........................ 0........................ 8
1/2........................ 0........................ 1........................ 9
= (1001000000)2
8) 65, base 3
Division........ Quotient........ Remainder(Digit)........ Digit #
65/3........................ 21........................ 2........................ 0
21/3........................ 7........................ 0........................ 1
7/3........................ 2........................ 1........................ 2
2/3........................ 0........................ 2........................ 3
= (2102)3
9) 5000, base 7
Division........ Quotient........ Remainder(Digit)........ Digit #
5000/7........................ 714........................ 2........................ 0
714/7........................ 102........................ 0........................ 1
102/7........................ 14........................ 4........................ 2
14/7........................ 2........................ 0........................ 3
2/7........................ 0........................ 2........................ 4
= (20402)7
10) 900, base 6
Division........ Quotient........ Remainder(Digit)........ Digit #
900/6 ........................150........................ 0........................ 0
150/6........................ 25........................ 0........................ 1
25/6........................ 4........................ 1........................ 2
4/6........................ 0........................ 4........................ 3
= (4100)6
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