In digital electronics, what is the highest-value seven-bit (7-bit) binary number when interpreted as an unsigned quantity?

Introduction:Seven-bit binary numbers are common in legacy character encodings and basic digital counters. The question asks for the highest-value number representable with 7 bits when interpreted as an unsigned quantity (no sign bit).

Given Data / Assumptions:

• Unsigned binary representation with exactly 7 bits.
• Bit positions range from b6 (MSB) to b0 (LSB).
• No sign or bias; pure base-2 magnitude.

Concept / Approach:For an n-bit unsigned integer, the minimum value is 0 and the maximum value is 2^n - 1. Setting all n bits to 1 yields the maximum value. For n = 7, the maximum is 2^7 - 1 = 128 - 1 = 127.

Step-by-Step Solution:

Verification / Alternative check:Write the place values: 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127. This matches 2^7 - 1.

Why Other Options Are Wrong:

• 128: Requires 8 bits (10000000₂); exceeds 7-bit range.
• 126: One less than maximum; binary 1111110₂.
• 125: Two less than maximum; binary 1111101₂.

Common Pitfalls:Confusing signed with unsigned. In signed 7-bit (two's complement is defined for 8-bit, not 7), ranges differ. Here we clearly use unsigned 7-bit magnitude.

Final Answer:127