Question

a mother makes a necklace to celebrate her daughter’s birthday. the necklace has beads for the birthday in binary using 1s and 0s. the part of the necklace that represents the day of the month is 11010. image of beads: 1,1,0,1,0 what is the decimal equivalent of that binary number?

Explanation:

Step1: Recall binary to decimal formula

To convert a binary number \( b_{n}b_{n - 1}\dots b_{1}b_{0} \) to decimal, we use the formula \( \sum_{i = 0}^{n}b_{i}\times2^{i} \), where \( b_{i} \) is the \( i \)-th digit (0 or 1) from the right (starting at 0). The binary number here is \( 11010 \) (5 digits, so positions 4 to 0 from left to right, or 0 to 4 from right to left: rightmost digit is position 0).

Step2: Identify each digit and its position

For \( 11010 \):

• Position 4 (leftmost): \( 1 \), value \( 1\times2^{4} \)
• Position 3: \( 1 \), value \( 1\times2^{3} \)
• Position 2: \( 0 \), value \( 0\times2^{2} \)
• Position 1: \( 1 \), value \( 1\times2^{1} \)
• Position 0 (rightmost): \( 0 \), value \( 0\times2^{0} \)

Step3: Calculate each term

• \( 1\times2^{4}=1\times16 = 16 \)
• \( 1\times2^{3}=1\times8 = 8 \)
• \( 0\times2^{2}=0\times4 = 0 \)
• \( 1\times2^{1}=1\times2 = 2 \)
• \( 0\times2^{0}=0\times1 = 0 \)

Step4: Sum the terms

Add the calculated values: \( 16 + 8 + 0 + 2 + 0 = 26 \)

Answer:

26