Convert the decimal (base 10) number 101 into its equivalent representation in binary (base 2).

Introduction / Context:
This problem is about number system conversion, specifically converting a decimal number into binary form. Understanding this conversion is important in computer science and digital logic, because computers internally represent numbers in binary.

Given Data / Assumptions:
- We are given the decimal number 101.
- We need to convert 101 from base 10 to base 2.
- The result should be expressed as a binary string of 0s and 1s.

Concept / Approach:
The standard method to convert a decimal number to binary is to repeatedly divide the number by 2, keeping track of the remainders. The binary representation is then obtained by reading the remainders from last to first. Alternatively, we can express the number as a sum of powers of 2 and read off which powers are present.

Step-by-Step Solution:
Step 1: Start with 101 and divide by 2: 101 / 2 = 50 with remainder 1.Step 2: Divide 50 by 2: 50 / 2 = 25 with remainder 0.Step 3: Divide 25 by 2: 25 / 2 = 12 with remainder 1.Step 4: Divide 12 by 2: 12 / 2 = 6 with remainder 0.Step 5: Divide 6 by 2: 6 / 2 = 3 with remainder 0.Step 6: Divide 3 by 2: 3 / 2 = 1 with remainder 1.Step 7: Divide 1 by 2: 1 / 2 = 0 with remainder 1, and stop because the quotient is now 0.Step 8: Write the remainders in reverse order of computation: 1 1 0 0 1 0 1, which is 1100101 in binary.

Verification / Alternative check:
Check by converting 1100101 back to decimal using binary place values. Starting from the right, the bits correspond to 1, 2, 4, 8, 16, 32, and 64. The binary number 1100101 has ones in positions for 64, 32, 4, and 1. So the value is 64 + 32 + 4 + 1 = 101. This confirms that 1100101 is the correct binary representation of 101.

Why Other Options Are Wrong:
Option 1100111 corresponds to 64 + 32 + 4 + 2 + 1 = 103. Option 1101001 corresponds to 64 + 32 + 8 + 1 = 105. Option 1101011 corresponds to 64 + 32 + 8 + 2 + 1 = 107. Option 1010001 corresponds to 64 + 16 + 1 = 81. None of these equal 101 in decimal.

Common Pitfalls:
Some learners write the remainders in the wrong order, reading from first to last instead of last to first. Others forget to continue dividing until the quotient becomes zero. It is also easy to miscalculate the decimal value of a candidate binary string if the place values are not correctly applied.

Final Answer:
The binary (base 2) representation of the decimal number 101 is 1100101.