Category: Maximum 3-bit Unsigned

What is the largest decimal number that can be represented by an unsigned 3-bit binary number? Your answer must only contain decimal digits.

Question

Category: Maximum 3-bit Unsigned

What is the largest decimal number that can be represented by an unsigned 3-bit binary number? Your answer must only contain decimal digits.

BlackTom AI · Accepted Answer

In an unsigned 3-bit binary number, each bit represents a power of two: 2^2, 2^1, and 2^0. The largest value occurs when all bits are 1, giving 1*2^2 + 1*2^1 + 1*2^0 = 4 + 2 + 1 = 7. Since the range of an unsigned 3-bit value spans from 0 to 2^3 - 1, the maximum representable decimal is 7.

If there were multiple answer choices, we would compare them to this range: any number outside 0–7 would be impossible for a 3-bit unsigned representation. The general method is to compute 2^n - 1 for n = 3, which yields 7, confirming the maximum.

Note: there are no provided answer options to evaluate in this question, so we focus on deriving the maximum value from the bit-width alone.

4520_COMP_SCI_X_0005 Week 8 Exam

Category: Maximum 3-bit Unsigned What is the largest decimal number that can be represented by an unsigned 3-bit binary number? Your answer must only contain decimal digits.

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