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MTH 120 - Changing from Base 10 to Another Base

MTH 120 - Changing from Base 10 to Another Base - Changing...

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Changing a whole number, e.g., 43, from Base 10 to Base 2 The first step is to find the largest power of 2 that is less than 43. So let’s review the powers of 2: 2 0 = 1 2 2 = 4 2 4 = 16 2 6 = 64 2 1 = 2 2 3 = 8 2 5 = 32 2 7 = 128 Since 64 is larger than 43, we take one step back and use 32. “Why?” you ask, because it is the largest power of 2 that is still smaller than 43. The second step is to ask ourselves, “How many whole’ times, i.e., not partial or fractional times, can 32 go into 43?” 32 can go into 43 once or 1 time. “Why once and not twice?” Because, 1 x 32 = 32 and 32 is smaller than 43, which is good, and 2 x 32 = 64 and 64 is larger than 43, which is bad. Since 32 can go into 43 once or 1 time, we start our new “base 2” by writing down a 1… 1 Next, subtract 1 x 32 from 43… 43 – 1 x 32 = 11 Then, we move to the next lower power of 2, i.e., 16, and… Repeat the second step by asking ourselves, “How many ‘ whole’ times can 16 go into 11?” 16 can go into 11 0 times because 0 x 16 = 0 and
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