Question

Question Jameela 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 convert the binary numbers to decimal, we can use the following method:

• For the binary number 101:

  • The rightmost digit represents \(2^0\), the next represents \(2^1\), and the leftmost represents \(2^2\).
  • So, \(1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5\).
  • Therefore, 101 in binary is 5 in decimal.

• For the binary number 1111:

  • The rightmost digit represents \(2^0\), the next represents \(2^1\), the next represents \(2^2\), and the leftmost represents \(2^3\).
  • So, \(1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 4 + 2 + 1 = 15\).
  • Therefore, 1111 in binary is 15 in decimal.

Thus, Jameela needs 5 notebooks and 15 apples for her field trip.

The correct response is: five notebooks and 15 apples.