Question about Mathsoft StudyWorks! Mathematics Deluxe 5.0 (11513) for PC

# 1111 base 2 + 1010 base 2 my answers are either 20 or 30

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• c64310 Feb 03, 2010

How would I work this problem

• May 11, 2010

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You can solve this the same way you solve regular base 10 addition. In base 10, if you add two numbers and the result is greater than 10, you carry a 1 to the next column to the left. So 6+3=9 (no carry), but 6+5=11 (we carried a 1 to the next column).

In base 2, there are only 2 digits to use (0 and 1) and we carry when the result is greater than 2. So in base 2, 1+0=1 (no carry), but 1+1=10 (carry to the next column).

In the 1's column, 1+0=1, no carry
In the 2's column, 1+1=0, carry 1 left
In the 4's column, 1+0+1(the carry from before)=0, carry 1 left
and so on.

It's easier than base 10, with only two digits to deal with.

Posted on Feb 03, 2010

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Neither of your guesses are correct.

1111 = ((1*2+1)*2+1)*2+1
1010 = ((1*2+0)*2+1)*2+0

Since the sum of the "low-order" bits (one '1' plus one '0') is an "odd" number, neither "20" ("even" number) nor "30" (another "even" number) could be the correct answer.

Posted on Feb 03, 2010

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