What is the decimal equivalent to the binary number 1011?

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BlackTom AI · Accepted Answer

Question restatement: What is the decimal equivalent to the binary number 1011?

Step 1: Recognize that each binary digit represents a power of two, starting from the rightmost bit (least significant bit). The binary number 1011 has four bits, corresponding to 2^3, 2^2, 2^1, and 2^0.

Step 2: Map each bit to its place value and multiply by the corresponding power of two:
- The leftmost bit is 1 at 2^3, contributing 1 × 2^3 = 8.
- The next bit is 0 at 2^2, contributing 0 × 2^2 = 0.
- The next bit is 1 at 2^1, contributing 1 × 2^1 = 2.
- The rightmost bit is 1 at 2^0, contributing 1 × 2^0 = 1.

Step 3: Add these contributions together to obtain the decimal value: 8 + 0 + 2 + 1 = 11.

Step 4: Note on options: Since no answer choices were provided in the prompt, we cannot evaluate alternative selections here. If options were present, one would compare each option to the computed decimal value (11) and identify the option that matches this result.

Additional clarifications: This method is the standard base conversion technique from binary to decimal, using place-value weights of powers of two. A quick cross-check is to group bits or to perform successive doubling-and-adding, but summing the weighted bits directly provides a transparent and scalable approach.

I&C SCI 10 LEC A: HOW ... Lecture 4 Pre-Work: Binary Numbers

What is the decimal equivalent to the binary number 1011?

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