SOLUTION: Name: MAT 145: Topics In Contemporary Math Bases Convert each of the following numbers into base-10 numbers. 1) 11000101(2) 2) 10011010(2) 3) 1023(5

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Question 1192159: Name: MAT 145: Topics In Contemporary Math

Bases
Convert each of the following numbers into base-10 numbers.
1) 11000101(2)
2) 10011010(2)
3) 1023(5)
4) 10053(7)
5) 32102(4)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
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1)
%2811000101%29%2810%29
2) %0D%0A10011010%2810%29
3)
1023%285%29=1%2A+5%5E3+%2B+0+%2A+5%5E2+%2B+2+%2A+5%5E1+%2B+3%2A5%5E0=%28138%29%2810%29
4)
10053%287%29=+1%2A7%5E4%2B0%2A7%5E3%2B0%2A7%5E2%2B5%2A7%5E1%2B3%2A7%5E0=%282439%29%2810%29
5)
32102%284%29=3%2A4%5E4%2B2%2A4%5E3%2B1%2A4%5E2%2B0%2A4%5E1%2B2%2A4%5E0=%28914%29%2810%29


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The student should understand the method shown by the other tutor for doing these conversions, because it helps the student learn about place values in different bases.

However, the method shown is inefficient, especially for numbers with many digits, since it requires knowing all the powers of the given base. There is a much more efficient method for doing these conversions.

Here is the algorithm:
start from the leftmost digit and
(1) multiply by the base and add the next digit;
(2) repeat (1) until all digits have been used

Here are the calculations for your 3rd example, 1023 base 5:

1*5=5; 5+0=5
5*5=25; 25+2=27
27*5=135; 135+3=138

And for your 4th example, 10053 base 7:

1*7=7; 7+0=7
7*7=49; 49+0=49
49*7=343; 343+5=348
348*7=2436;2436+3=2439

And your last, 32102 base 4:

3*4=12; 12+2=14
14*4=56; 56+1=57
57*4=228; 228+0=228
228*4=912; 912+2=914