Binary conversion practice — base-10 to base-2 Convert the decimal number 64 (base 10) into its binary representation (base 2).

Introduction / Context:
Converting between decimal (base 10) and binary (base 2) is a foundational digital electronics and computer science skill. The goal is to represent the same quantity using powers of 2 rather than powers of 10. Here we convert 64 in decimal to its binary form, reinforcing the idea that each binary digit (bit) corresponds to a power of 2 position.

Given Data / Assumptions:

• Input value: 64 in base 10.
• We need an unsigned binary result.
• No leading sign bit is required; leading zeros may be included to match option widths.

Concept / Approach:

Binary expansion expresses a number as a sum of powers of 2. Identify the highest power of 2 less than or equal to the number, set that bit to 1, and set all lower bits to 0 if no remainder remains. Alternatively, repeated division by 2 provides the bit pattern from least significant bit to most significant bit.

Step-by-Step Solution:

Verification / Alternative check:

Convert 01000000 back to decimal using positional weights: 02^7 + 12^6 + 02^5 + … + 02^0 = 64. This confirms correctness.

Why Other Options Are Wrong:

01010010 represents 2^6 + 2^4 + 2^1 = 64 + 16 + 2 = 82, not 64.

00110110 equals 32 + 16 + 4 + 2 = 54.

01001000 equals 64 + 8 = 72.

Common Pitfalls:

Confusing bit positions, miscounting the number of leading zeros, or assuming every answer must be a power of 2 pattern. Always confirm by summing powers of 2 with bit positions set to 1.

Final Answer:

01000000