Significance of bit positions in binary numbers Which bit change causes the largest change in a binary number's value: MSB (most significant bit) or LSB (least significant bit)?

Introduction / Context:
Each bit in a binary number represents a power of 2. The contribution of a bit to the total numeric value depends on its position. Understanding which position has the greatest impact is key to topics like quantization error, fixed-point formats, and digital signal processing dynamic range.

Given Data / Assumptions:

• Binary positional weights: bit i contributes 2^i when set.
• MSB is the highest-order bit in the representation.
• LSB is the lowest-order bit (2^0 place).

Concept / Approach:

Because weights increase exponentially with position, toggling the MSB changes the value by the largest amount among bits in the same width. In contrast, toggling the LSB changes the value by only 1. Non-bit terms like “frequency” and “duty cycle” relate to signals, not numeric bit significance.

Step-by-Step Solution:

Verification / Alternative check:

Example with 8 bits: MSB weight is 128, LSB is 1. Flipping the MSB changes the number by 128, far exceeding any other single bit flip.

Why Other Options Are Wrong:

Frequency and duty cycle describe time-domain waveform characteristics, not positional numeric significance.

LSB change is the smallest possible change (±1) in an unsigned representation.

Common Pitfalls:

Confusing signed magnitude or two’s complement sign semantics with numeric weight; even there, the sign/MSB still dominates magnitude effect for a given width. Always relate position to its 2^i weight.

Final Answer:

MSB