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?

Question

(1 point)

four notebooks and 10 apples

Ofive notebooks and 15 apples

101 notebooks and 1,111 apples

25 notebooks and eight apples

Answer 1

To decode the binary numbers Jameela used:

• "101" in binary is equal to \(1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5\). So, she needs 5 notebooks.

• "1111" in binary is equal to \(1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 4 + 2 + 1 = 15\). So, she needs 15 apples.

Thus, Jameela really needs 5 notebooks and 15 apples.

The correct choice is: five notebooks and 15 apples.