Chapter 3: Signed and Unsigned Numbers
### 3.1 Introduction
In assembly language programming, numbers can be classified as signed or unsigned, which significantly impacts how they are represented and manipulated. This chapter explores the concepts of signed and unsigned numbers, their representation in binary, and the implications for arithmetic operations.
### 3.2 Binary Representation of Numbers
#### 3.2.1 Unsigned Binary Representation
- **Range:**
- Represents only non-negative values.
- For an n-bit binary number, the range is \(0\) to \(2^n - 1\).
- **Example:**
- \(8\)-bit unsigned binary can represent values from \(0\) to \(255\).
#### 3.2.2 Signed Binary Representation (Two's Complement)
- **Range:**
- Represents both positive and negative values.
- For an n-bit binary number in two's complement, the range is \(-2^{n-1}\) to \(2^{n-1} - 1\).
- **Example:**
- \(8\)-bit signed binary can represent values from \(-128\) to \(127\).
### 3.3 Sign Extension
- **Sign Extension:**
- Process of expanding a signed binary number to a larger size while preserving its sign.
- **Example:**
- Sign-extending \(1101\) (4-bit) to \(11111101\) (8-bit).
### 3.4 Arithmetic Operations
#### 3.4.1 Unsigned Arithmetic
- **Addition:**
- Standard binary addition.
- **Subtraction:**
- Standard binary subtraction.
#### 3.4.2 Signed Arithmetic
- **Addition:**
- Follows the same rules as unsigned addition.
- **Subtraction:**
- Subtraction is often performed using two's complement.
### 3.5 Overflow
- **Overflow:**
- Occurs when the result of an arithmetic operation is too large to be represented.
- **Detection:**
- Overflow is detected by examining the carry into and out of the sign bit.
### 3.6 Conditional Jump Instructions
- **Conditional Jumps:**
- Instructions that jump to a specified location based on a condition.
- **Example:**
- Jump if overflow (`jo`), jump if not overflow (`jno`).
### 3.7 Conclusion
Understanding the distinction between signed and unsigned numbers is crucial for accurate arithmetic operations in assembly language. As you work with different data types, be mindful of the implications of signedness on your calculations.
Comments
Post a Comment