Question

a computer scientist creates a necklace to celebrate the birth of her daughter. the necklace encodes her daughter’s birthday in binary using silver 1 and 0 beads. the part of the necklace that encodes the day of the month is 11010. image of beads what is the decimal equivalent of that binary number? your answer should be an integer, like 6 related content 0100 0010 binary numbers 1100 1010 article

Explanation:

Step1: Identify binary digits positions

The binary number is \(11010\), from right (LSB) to left (MSB), positions are \(4,3,2,1,0\) (wait, actually positions are \(4,3,2,1,0\) but values are \(2^4, 2^3, 2^2, 2^1, 2^0\) for digits from left to right? Wait no: for binary number \(d_4d_3d_2d_1d_0\) (left to right), the value is \(d_4\times2^4 + d_3\times2^3 + d_2\times2^2 + d_1\times2^1 + d_0\times2^0\). So \(11010\) has digits (left to right) \(d_4 = 1\), \(d_3 = 1\), \(d_2 = 0\), \(d_1 = 1\), \(d_0 = 0\).

Step2: Calculate each term

• \(d_4\times2^4 = 1\times16 = 16\)
• \(d_3\times2^3 = 1\times8 = 8\)
• \(d_2\times2^2 = 0\times4 = 0\)
• \(d_1\times2^1 = 1\times2 = 2\)
• \(d_0\times2^0 = 0\times1 = 0\)

Step3: Sum the terms

Sum: \(16 + 8 + 0 + 2 + 0 = 26\)

Answer:

26