Question

q4) 1101 in binary is equivalent to which of the following decimal sums? * 1 point ○ 8+4+1 ○ 8+4+2 ○ 8+4+2+1

Explanation:

Step1: Recall binary to decimal conversion

To convert a binary number to decimal, we use the place values which are powers of 2. For a 4 - bit binary number \(b_3b_2b_1b_0\) (from left to right), the decimal value is \(b_3\times2^{3}+b_2\times2^{2}+b_1\times2^{1}+b_0\times2^{0}\).
For the binary number \(1101\), \(b_3 = 1\), \(b_2=1\), \(b_1 = 0\), \(b_0=1\).

Step2: Calculate each term

• For \(b_3 = 1\) and \(2^{3}=8\), the term is \(1\times8 = 8\).
• For \(b_2 = 1\) and \(2^{2}=4\), the term is \(1\times4=4\).
• For \(b_1 = 0\) and \(2^{1}=2\), the term is \(0\times2 = 0\).
• For \(b_0 = 1\) and \(2^{0}=1\), the term is \(1\times1 = 1\).

Step3: Sum the non - zero terms

The sum of the non - zero terms (since the term for \(b_1\) is zero) is \(8 + 4+1\).

Answer:

\(8 + 4+1\) (corresponding to the first option)