What is the range of decimal values that can be represented using 11 binary bits

The range of decimal values that can be represented using 11 binary bits depends on whether the binary numbers are considered **unsigned** or **signed**.

### 1. **Unsigned binary:**
For an unsigned binary number, all bits are used to represent the magnitude of the number. The range is from 0 to the maximum value that 11 bits can hold.

- The minimum value is 0.
- The maximum value is \( 2^{11} - 1 = 2047 \).

Thus, the range for **unsigned 11-bit binary numbers** is:
\[ \boxed{0 \text{ to } 2047} \]

### 2. **Signed binary (Two's complement):**
In two's complement representation, the first bit is used to indicate the sign (0 for positive, 1 for negative), and the remaining bits represent the magnitude.

- The minimum value is \( -2^{(11-1)} = -2^{10} = -1024 \).
- The maximum value is \( 2^{(11-1)} - 1 = 1024 - 1 = 1023 \).

Thus, the range for **signed 11-bit binary numbers** is:
\[ \boxed{-1024 \text{ to } 1023} \]

### Summary:
- **Unsigned:** 0 to 2047
- **Signed (Two's complement):** -1024 to 1023

Would you like more details on this or help with a similar topic?

### Related Questions:
1. How do you represent negative numbers in two's complement?
2. How does the range of values change if more bits are used?
3. How does the binary representation differ between signed and unsigned numbers?
4. What are some common uses of two's complement in computing?
5. How can you convert a decimal number to an 11-bit binary number?

### Tip:
When working with binary, always clarify if the system uses **signed** or **unsigned** representation, as it affects the range and interpretation of the numbers.

What is the range of decimal values that can be represented using 11 binary bits?

Understand the range of decimal values that can be represented using 11 binary bits. Learn about the differences between unsigned and signed (Two's complement) representations. This detailed explanation is suitable for high school students learning binary systems.

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