In digital systems, how many distinct bit combinations (unique patterns) are possible in one byte, that is in 8 bits?

Introduction / Context:
The byte is a fundamental unit of information in digital electronics and computer systems. A byte is defined as a group of eight bits. Each bit can independently take one of two possible values, usually denoted 0 and 1. Understanding how many distinct values a byte can represent is essential in topics such as data representation, memory capacity and encoding schemes.

Given Data / Assumptions:

We know that a byte is exactly 8 bits in almost all modern systems.
Each bit has two possible states: 0 or 1.
All bits are independent, so every combination of bit values is possible.
The question asks for the total number of unique bit patterns in an 8 bit group.
We assume ordinary binary counting with no additional constraints.

Concept / Approach:
When you have a certain number of independent binary choices, the total number of combinations is found using powers of two. One bit has 2 possible states. Two bits have 2 * 2 = 2^2 combinations. In general, n bits have 2^n combinations. For a byte with 8 bits, the total number of different bit patterns is 2^8. Evaluating 2^8 gives 256. This means a single byte can represent 256 distinct values, often numbered from 0 to 255 in unsigned representation.

Step-by-Step Solution:
Step 1: Identify that there are 8 bits in a byte. Step 2: Note that each bit can be either 0 or 1, giving 2 possibilities per bit. Step 3: Because the bits are independent, multiply the number of possibilities for each bit: total combinations = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2. Step 4: Express this product as a power: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^8. Step 5: Compute 2^8 by repeated doubling: 2^4 = 16, 2^5 = 32, 2^6 = 64, 2^7 = 128 and 2^8 = 256. Step 6: Conclude that there are 256 distinct bit combinations in one byte.

Verification / Alternative check:
You can verify this result by thinking about the numeric range of an unsigned byte in many programming languages. For example, an unsigned eight bit variable typically holds values from 0 to 255 inclusive. This is 256 distinct values because the count includes zero. Another sanity check is to realise that adding one more bit doubles the number of combinations. A seven bit quantity represents 2^7 = 128 values; adding the eighth bit doubles this to 256 values, consistent with the power of two formula.

Why Other Options Are Wrong:
Eight combinations would correspond to only three bits, since 2^3 = 8, not to a full byte.
Sixteen combinations correspond to four bits (2^4 = 16).
One hundred twenty eight combinations correspond to seven bits (2^7 = 128). All of these are less than the 2^8 combinations of a byte.

Common Pitfalls:
Beginners sometimes confuse bits and bytes and may mistakenly think that a byte can represent only 8 or 16 different values because it has eight bits. Another pitfall is to forget that binary counting starts at zero, so the highest value for an unsigned eight bit number is 255, but that still counts as 256 distinct values. Remembering the simple rule that n bits give 2^n combinations helps avoid such errors.

Final Answer:
One byte, or 8 bits, can represent 256 different bit combinations.