Convert the binary number 1101111 to its decimal (base 10) equivalent.

Introduction / Context:
This is a basic computer science and number systems question that asks for conversion of a binary number to its decimal form. Understanding positional notation and powers of 2 is crucial for this type of conversion.

Given Data / Assumptions:
- The binary number given is 1101111.
- We must convert this binary representation into its decimal (base 10) value.
- In binary, each digit represents a power of 2, starting from 2^0 at the rightmost position.

Concept / Approach:
To convert from binary to decimal, we expand the binary number as a sum of powers of 2, including only those positions where the binary digit is 1. The general form for a binary number b6 b5 b4 b3 b2 b1 b0 is b6 * 2^6 + b5 * 2^5 + ... + b0 * 2^0.

Step-by-Step Solution:
Write 1101111 as digits from left to right: 1 1 0 1 1 1 1. Label powers of 2 from right to left: 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6. Match digits to powers: 1 * 2^6, 1 * 2^5, 0 * 2^4, 1 * 2^3, 1 * 2^2, 1 * 2^1, 1 * 2^0. Compute each non zero term: 1 * 2^6 = 64, 1 * 2^5 = 32, 1 * 2^3 = 8, 1 * 2^2 = 4, 1 * 2^1 = 2, 1 * 2^0 = 1. Add them: 64 + 32 + 8 + 4 + 2 + 1 = 111.

Verification / Alternative Check:
We can also group intermediate sums: 64 + 32 = 96, 96 + 8 = 104, 104 + 4 = 108, 108 + 2 = 110, and finally 110 + 1 = 111. Another quick check is to use a calculator that supports binary to decimal conversion, but the stepwise method helps reinforce understanding of positional notation.

Why Other Options Are Wrong:
101 corresponds to a different binary representation and is too small compared to 111.
110 is also smaller and would come from a slightly different binary pattern.
100 is even smaller and incorrect for this specific binary number.
115 is larger than the computed sum and does not correspond to 1101111 in binary.

Common Pitfalls:
Students sometimes misalign the powers of 2, starting from 2^1 instead of 2^0 at the rightmost bit. Others add incorrect powers or miscalculate exponents such as 2^5 or 2^6. Remembering that binary is base 2 and carefully mapping each bit to its power of 2 helps avoid mistakes.

Final Answer:
The decimal equivalent of binary 1101111 is 111.