What is the decimal equivalent of the binary number 1101?

What is the decimal equivalent of the binary number 1101?

• A. 12
• B. 13
• C. 14
• D. 15

Answer: (B)

To understand why the decimal equivalent of the binary number 1101 is 13, we can break it down by analyzing the binary system. Each digit in a binary number represents an increasing power of 2, starting from the rightmost digit, which corresponds to \(2^0\). In the binary number 1101, we can lay it out as follows: - The leftmost digit '1' is in the \(2^3\) place, which equals 8. - The next digit '1' is in the \(2^2\) place, which equals 4. - The next digit '0' is in the \(2^1\) place, which equals 0. - The rightmost digit '1' is in the \(2^0\) place, which equals 1. Now, we add these values together: - \(8 \, (from \, 2^3)\) - \(+ 4 \, (from \, 2^2)\) - \(+ 0 \, (from \, 2^1)\) - \(+ 1 \, (from \, 2^0)\) When we sum them up

To understand why the decimal equivalent of the binary number 1101 is 13, we can break it down by analyzing the binary system. Each digit in a binary number represents an increasing power of 2, starting from the rightmost digit, which corresponds to (2^0).

In the binary number 1101, we can lay it out as follows:

• The leftmost digit '1' is in the (2^3) place, which equals 8.

• The next digit '1' is in the (2^2) place, which equals 4.

• The next digit '0' is in the (2^1) place, which equals 0.

• The rightmost digit '1' is in the (2^0) place, which equals 1.

Now, we add these values together:

• (8 , (from , 2^3))

• (+ 4 , (from , 2^2))

• (+ 0 , (from , 2^1))

• (+ 1 , (from , 2^0))

When we sum them up