Understanding Sign-Extension in Computer Architecture

What does sign-extending a data item entail?

• A. Replicating the low-order sign bit
• B. Increasing the size by adding zeros
• C. Replicating the high-order sign bit
• D. Reducing the size of data item

Answer: (C)

Sign-extending a data item involves replicating the high-order sign bit, which is the leftmost bit that indicates the sign of a number in a signed binary representation. When a smaller signed integer is converted to a larger size, such as from 8 bits to 16 bits, the sign bit is extended to maintain the correct numerical value. This process ensures that negative numbers remain negative and positive numbers remain positive after the data type expansion. For example, if you have an 8-bit signed integer with a binary value of 11111101 (which represents -3 in two’s complement), when sign-extending to 16 bits, the resulting value would be 11111111 11111101. Here, the sign bit (1) is replicated into the higher-order bits to keep the intended value intact. This is crucial in computing systems to ensure that arithmetic operations and other computations yield the expected results, especially when transitioning between data sizes.

When it comes to computer architecture, you might often hear terms that sound a lot like tech jargon. But don’t worry. Today, let’s break down a concept that’s key to understanding how computers interpret numbers: sign-extension. So, what exactly does it mean to sign-extend a data item? It’s more than just a quirky term; it’s a fundamental concept that ensures numbers remain coherent when they change in size.

To put it simply, sign-extension involves replicating the high-order sign bit, which is that all-important leftmost bit. This bit tells us whether a number is positive or negative in a signed binary representation. But hold up—why is this significant? Well, when we expand smaller signed integers to larger sizes (like converting from 8 bits to 16 bits), that high-order sign bit needs to be extended. This ensures the value stays true to its original sign after the expansion.

Let’s say you have an 8-bit signed integer, represented by the binary value 11111101. If we break it down, that value stands for -3 in two's complement form. Now, if we want to convert this number into a 16-bit binary format, we would replicate the sign bit (which is 1, indicating that it’s a negative number). So the resulting value after sign-extension becomes 11111111 11111101. See what happens here? The leftmost bits fill up with 1s to maintain the negativism of the original number.

Understanding this process isn’t just an abstract academic exercise; it’s vital for how arithmetic operations work in computing systems. Imagine if a negative number accidentally turned into a positive number during programming; that would lead to some chaotic miscalculations!

So the next time you are plugging away at studying for your WGU ICSC3120 C952 exam, keep in mind how pivotal sign-extension is. It’s all about ensuring the integrity of numbers amidst the ever-shifting landscape of data types. And remember, as you prep for that practice exam, grasping these concepts solidifies your foundation in computer architecture—essential for snatching up those concepts like a pro!

Whether you're a seasoned programmer or just starting in computer science, you know what? Understanding sign-extension will help you solve puzzles that fall under the realm of digital data. It’s not just about numbers—it's about making those numbers work for you in the digital world!