Sign Bit Extension Explained with Examples

Understanding how numbers are stored and manipulated in binary is crucial in electronics, embedded systems, and computer architecture. One important concept in this area is Sign Bit Extension—especially when dealing with signed numbers and different bit widths.

In this blog, we’ll break it down in a simple way with clear examples to help you grasp it fully.


What is Sign Bit Extension?

Sign Bit Extension (also called Sign Extension) is the process of increasing the number of bits of a binary number while preserving its sign (positive or negative). This is commonly used when converting a signed number from a smaller bit size (like 8 bits) to a larger one (like 16 bits or 32 bits).

Rule:
  • If the number is positive (MSB is 0), pad with 0s on the left.
  • If the number is negative (MSB is 1), pad with 1s on the left.

This keeps the value the same even in the larger bit size.

Why is Sign Bit Extension Needed?

In embedded systems and low-level programming (like Arduino, microcontrollers, or assembly), we often deal with:

  • Different variable sizes (e.g., int8_t to int16_t)
  • Arithmetic operations between different bit widths
  • Preserving negative values during conversion

Without sign extension, negative numbers can become incorrect when extended.

Examples of Sign Bit Extension

Example 1: Extending +5 (8-bit to 16-bit)

8-bit: 00000101 (MSB is 0 → positive)

Now extend it to 16 bits → just pad zeros on the left.

16-bit: 00000000 00000101

Decimal value: still +5

Example 2: Extending -5 (8-bit to 16-bit)

8-bit: 11111011 (MSB is 1 → negative)

Pad ones on the left to keep the sign:

16-bit: 11111111 11111011

Still represents -5 in 2's complement 16-bit.

Example 3: Arduino Use Case

Let’s say you're reading a signed sensor value stored in an 8-bit register, but your program expects a 16-bit integer.
If the value is 0xFB (which is -5), and you just convert it like this:

uint8_t val8 = 0xFB;
int16_t val16 = val8; // WRONG: value becomes +251

To correctly extend the sign:

int8_t val8 = 0xFB;
int16_t val16 = (int16_t) val8; // CORRECT: value remains -5

General Formula (for reference)

If MSB = 1 and original width = n bits, extend by adding (m - n) 1s in front (m = new width).

If MSB = 0, extend with 0s.

Real-World Applications

  • Sensor Data Conversion:
    Signed 8-bit sensor outputs often need to be processed in 16 or 32 bits.

  • Microcontroller Arithmetic:
    When combining values from different registers, incorrect extension can cause bugs.

  • Assembly Programming:
    MOVSX (move with sign extension) and MOVZX (zero extension) instructions in x86 are based on this concept.

Key Takeaways

  • Sign extension is essential for preserving the value of signed numbers when changing bit width.

  • Always check if the number is signed before extending.

  • In Arduino/C programming, incorrect sign extension can cause logic errors.

Stay tuned to hobitronics.blog

To know more about Binary Data Representation - Click here!


Comments

Post a Comment

Popular posts from this blog

Why Does My Old Phone Charge Slowly But Heat Up More?

Image
The Truth About Aging Batteries Welcome back to Hobitronics — where we decode the daily mysteries inside your gadgets. Today we’re getting into something everyone with a 3-year-old smartphone has asked themselves: "Why is my phone charging so slow? And why does it feel like it’s cooking itself while doing it?" You’re not imagining it. Aging phones really do charge slower and heat up more — and the reason lies deep inside the battery chemistry , internal resistance , and the invisible wear and tear of thousands of charging cycles. 1. Your Battery Ages — Even If It Looks Fine Smartphones use Li-ion or Li-Po batteries . These are fantastic when new, but over time: Electrochemical reactions degrade the anode/cathode SEI (Solid Electrolyte Interface) layer thickens Lithium plating reduces active ions Capacity drops with every charge-discharge cycle This degradation results in something very important: higher internal resistance . 2. Internal Resistance: Th...
Read more

Why Do Phone Chargers Get Hot While Charging?

Image
Welcome back to Hobitronics — where we decode the daily mysteries inside your gadgets. Today we’re talking about something everyone has noticed at some point: Why does your phone charger heat up when you're using it? — and why do the cheap ones feel like they might just melt? That warmth isn’t just you imagining things. It’s real, and it’s telling you something about what’s happening inside the plastic shell of that adapter. Especially with budget chargers, the heat is more than a minor annoyance — it’s a sign of energy loss , sloppy design , and sometimes, real danger. 1. What's Actually Inside a Charger? Your phone charger might look like a simple plug, but it’s actually a clever little Switch Mode Power Supply (SMPS) . It takes the high-voltage AC from your wall and transforms it into a low-voltage, phone-friendly DC output. Here’s the quick path: 230V AC in → DC conversion → stepped-down voltage → regulated output Key parts of a charger includes: Bridge Rect...
Read more

Pulse Code Modulation (PCM): The Digital Backbone of Modern Communication

Image
Introduction: Why PCM Matters In the era of smartphones, digital streaming, and cloud-based communication, it's easy to forget that all digital information starts out analog. Whether it’s your voice, your favorite song, or a movie’s soundtrack, sound begins as a continuously varying signal. But to store, transmit, or process it digitally, we need to convert it into a digital form—and that's where Pulse Code Modulation (PCM) comes in. PCM is the foundation of digital audio , and it plays a crucial role in telecommunications, media storage, and even space communication. Let’s dive deep into how it works, why it’s important, and where it’s used. What is PCM? Pulse Code Modulation (PCM) is a method used to digitally represent analog signals. It involves sampling , quantizing , and encoding an analog input into a binary form suitable for transmission or storage. Think of PCM as translating a wave of sound into a digital language that machines can understand. The Three Core P...
Read more

Why Does Tea Taste Weird on an Induction Stove?

Image
Science Behind the Taste Change Welcome to the Hobitronics blog — a space where everyday curiosities about electronics and appliances get the deep respect they deserve. You're not just asking "Why does tea taste off when I use an induction stove?" You're asking one of the most nuanced, beautifully human questions: "What really happens under the hood of our everyday devices?" And that is exactly what Hobitronics is here for — to make the complex beautiful, relatable, and fun. This is part of our series where we decode the science of consumer electronics that people use every day but rarely understand. So let’s talk about tea☕. Me? Personally? My day doesn't start without a hot cup of tea. No offense to the coffee gang, but my favorite will always be the simple, soul-healing cup of tea. But if you’ve ever made tea on an induction stove ... you might’ve noticed something strange: It overboils too quickly The tea turns slightly bitter The milk...
Read more

Delta Modulation and Adaptive Delta Modulation: Simplifying Digital Voice Communication

Image
In the world of digital communication, Pulse Code Modulation (PCM) paved the way for digitizing analog signals. However, PCM isn't always efficient in terms of bandwidth and data rate. To address these limitations, two intelligent techniques were developed: Delta Modulation (DM) and its improved version, Adaptive Delta Modulation (ADM) . In this blog, we’ll take a deep dive into how Delta Modulation works, its advantages and limitations, and how Adaptive Delta Modulation overcomes those challenges. So, let’s decode this modulation magic! 🔁 Recap: What Came Before — PCM Before we explore DM and ADM, it’s essential to remember what PCM  (ref:  Pulse Code Modulation (PCM): The Digital Backbone of Modern Communication ) does: Samples the analog signal at regular intervals (Nyquist Rate). Quantizes the samples into discrete values. Encodes these values into binary for transmission. While PCM is powerful, it requires a high bit rate and complex quantization , makin...
Read more

🎧 Sampling and Quantization Explained

Image
Welcome back to Hobitronics , your go-to space for demystifying electronics and communication concepts with clarity and creativity. Today, we begin a fundamental journey through how analog signals become digital , forming the bedrock of everything from your voice call to digital music and embedded sensor systems. We’ll dive deep into the two most critical steps: Sampling and Quantization . These processes are essential for converting real-world continuous signals into digital data that machines can store, process, and transmit. 🌊 The Real-World is Analog Most physical phenomena—sound, light, temperature, voltage—are analog in nature. This means they vary smoothly and continuously over time. But computers, microcontrollers, and communication systems operate in the digital domain —they understand only discrete values, especially binary (0s and 1s) . So how do we bridge this analog-digital divide? By converting analog signals into digital ones using Analog-to-Digital Conversion (...
Read more

Semiconductor Behavior at 0K vs. 300K:Energy Band Gap

Image
Energy Band Gap at 0K and 300K Understanding how the energy band gap of semiconductors like silicon and germanium changes with temperature is key to designing modern electronics. In this article, we explore how band gaps behave at 0K and 300K , how doping influences conduction , and their real-world applications in transistors, solar cells, and LEDs. Semiconductors like   silicon   and  germanium  have specific  energy band gaps  that determine how easily electrons can move from the  valence band  to the  conduction band . These materials exhibit different behavior at  different  temperatures Energy Band Gap of Semiconductors at Different Temperatures Silicon : At 0K :  The energy band gap in silicon is around  1.21 eV .  At this temperature, electrons are  tightly bound  to their atoms, and no electrons have  enough energy to jump across the gap . Thus,  no conduction  occurs,  and sil...
Read more

Controlling RGB LEDs with PWM Using Arduino

Image
P ulse Width Modulation (PWM) is not just a feature of microcontrollers — it’s a foundational technique in electronics. From dimming LEDs to simulating analog voltage levels, PWM is used in display systems , communication protocols , and motor drivers.  In this article, we’ll explore how PWM works technically and apply it to a fun and colorful project: controlling an RGB LED using an Arduino . Whether you’re an engineering student or a DIY hobbyist, this simple RGB LED demo will give you a hands-on feel for what PWM really means — both in concept and application. What is a Common Cathode RGB LED? An RGB LED combines three LEDs — Red, Green, and Blue — into a single package. In a common cathode RGB LED , all three internal LEDs share one ground (GND) pin. The remaining three pins individually control the red, green, and blue segments. By varying the amount of current (or rather, the voltage drop) across each color pin, you can create a wide spectrum of colors through additive...
Read more