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)

Answer 1

To decode Jameela's shopping list, we need to convert the binary numbers into decimal.

1. The binary number "101" is calculated as follows:
   • \(1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\)
   • \(= 1 \times 4 + 0 \times 2 + 1 \times 1\)
   • \(= 4 + 0 + 1 = 5\)

So, "101" in binary is 5 in decimal, which means Jameela needs 5 notebooks.

2. The binary number "1111" is calculated as follows:
   • \(1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)
   • \(= 1 \times 8 + 1 \times 4 + 1 \times 2 + 1 \times 1\)
   • \(= 8 + 4 + 2 + 1 = 15\)

So, "1111" in binary is 15 in decimal, which means Jameela needs 15 apples.

In summary, Jameela needs 5 notebooks and 15 apples.