Number systems conversion (digital electronics): convert the decimal value 89 (base 10) to its exact binary representation (base 2). Which of the following choices correctly equals 89 in binary?

Introduction / Context:Converting between decimal (base 10) and binary (base 2) is a foundational skill in digital electronics and computer architecture. The question asks for the binary representation of 89₁₀. Understanding this helps with addressing, masking, and low-level data manipulations.

Given Data / Assumptions:

• Target value: 89 in base 10.
• Binary uses powers of 2 (… 64, 32, 16, 8, 4, 2, 1).
• No sign bit or fractional components are involved.

Concept / Approach:The standard approach is repeated subtraction (or division by 2 remainders) using powers of 2. Express 89 as a sum of distinct powers of 2, then place 1s in those bit positions and 0s elsewhere. Highest power of 2 not exceeding 89 is 64 (2^6).

Step-by-Step Solution:

Verification / Alternative check:Compute 1011001₂ back to decimal: 64 + 16 + 8 + 1 = 89. This confirms correctness.

Why Other Options Are Wrong:

Common Pitfalls:Dropping leading zeros is fine, but do not drop necessary middle zeros; confusing the order of bits or mis-summing powers of 2 causes off-by-one errors.

Final Answer:1011001₂