What is the decimal equivalent of the binary number 0010011?

What is the decimal equivalent of the binary number 0010011?

• A. 10
• B. 19
• C. 21
• D. 35

Answer: (B)

To find the decimal equivalent of the binary number 0010011, it is essential to understand how binary numbers are structured. Each digit in a binary number represents a power of 2, starting from the rightmost digit (which is the least significant bit). In the binary number 0010011, we can break it down as follows: - The rightmost digit represents \(2^0\) (which is 1). - The second digit from the right represents \(2^1\) (which is 2). - The third digit represents \(2^2\) (which is 4). - The fourth digit represents \(2^3\) (which is 8). - The fifth digit represents \(2^4\) (which is 16). - The sixth digit represents \(2^5\) (which is 32). - The leftmost digit represents \(2^6\) (which is 64). Now, looking at the binary number 0010011, we only have 1s in the positions for \(2^1\) (2) and \(2^4\) (16). Therefore, we calculate: - The contribution from \(2^1\) is

To find the decimal equivalent of the binary number 0010011, it is essential to understand how binary numbers are structured. Each digit in a binary number represents a power of 2, starting from the rightmost digit (which is the least significant bit).

In the binary number 0010011, we can break it down as follows:

• The rightmost digit represents (2^0) (which is 1).

• The second digit from the right represents (2^1) (which is 2).

• The third digit represents (2^2) (which is 4).

• The fourth digit represents (2^3) (which is 8).

• The fifth digit represents (2^4) (which is 16).

• The sixth digit represents (2^5) (which is 32).

• The leftmost digit represents (2^6) (which is 64).

Now, looking at the binary number 0010011, we only have 1s in the positions for (2^1) (2) and (2^4) (16). Therefore, we calculate:

• The contribution from (2^1) is