Binary Adders: Building Arithmetic from Logic
In digital systems, addition isn’t just a mathematical operation—it’s a logic function built from gates. This page introduces binary adders, the foundational circuits that compute sums, carry bits, and enable arithmetic in processors, ALUs, and embedded devices.
You’ll start with the simplest building block—the Half Adder, which adds two single-bit inputs and outputs a sum and carry. Then, you’ll extend this to the Full Adder, which handles three inputs (including carry-in) and becomes the core unit for multi-bit addition.
What You’ll Learn
- Half Adder
- Logic diagram using XOR and AND gates
- Boolean expressions for sum and carry
- Truth table and output behavior
- Verilog HDL code
- Latency analysis
- Full Adder
- Constructed from two half adders and an OR gate
- Sum and carry-out logic
- Truth table and gate-level diagram
- Verilog HDL code
- Latency analysis
- Ripple Carry Adder
- Chaining full adders to add multi-bit binary numbers
- Propagation of carry from LSB to MSB
- Verilog HDL code
- Latency analysis
- Carry Lookahead Adder
- Speeding up addition by predicting carry bits
- Generate (G) and Propagate (P) logic
- Block-level diagram and Boolean expressions
- Latency analysis
- Comparison with ripple carry in terms of delay
Why Adders Matter
Adders are the first step toward computation. Whether you’re designing a calculator, a CPU, or a control system, binary addition is everywhere. Understanding how adders work—how they’re built from gates, how they handle carry, and how they scale—is essential for any digital designer.
This page connects directly to your earlier work with logic gates and Boolean simplification. You’ll see how XOR, AND, and OR gates combine to form arithmetic logic, and how propagation delay becomes a design constraint in multi-bit systems.
Visualizing Latency
You’ll also explore timing diagrams for ripple and lookahead adders, showing how input changes ripple through the circuit and affect output timing. These visualizations help you understand not just what the circuit does—but how fast it does it.