Question

ameela is learning about binary numbers. She leaves her mom an “encoded” shopping list that says she needs “101” notebooks and a bag of “1111” apples for her field trip. What does she really need? (1 point) Responses four notebooks and 10 apples four notebooks and 10 apples five notebooks and 15 apples five notebooks and 15 apples 101 notebooks and 1,111 apples 101 notebooks and 1,111 apples 25 notebooks and eight apples

Answer 1

To decode Ameela's shopping list, we need to convert the binary numbers "101" and "1111" into decimal (base 10) numbers.

1. Binary "101":

   • The binary system is base 2. The positions from right to left represent powers of 2:
     • \(2^0\) = 1 (rightmost digit)
     • \(2^1\) = 2
     • \(2^2\) = 4
   • So, "101" in binary translates to: \(1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5\)

2. Binary "1111":

   • Similarly, for "1111":
     • \(2^0\) = 1
     • \(2^1\) = 2
     • \(2^2\) = 4
     • \(2^3\) = 8
   • Thus, "1111" in binary translates to: \(1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 4 + 2 + 1 = 15\)

Putting it all together, Ameela needs 5 notebooks and 15 apples for her field trip.

So the correct response is: five notebooks and 15 apples.