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 Understanding Boolean Logic Before we can build logic gates or design digital systems, we need to understand the language that describes how they work,  Boolean logic . What Is Boolean Logic? Boolean logic is a type of algebra that deals with true or false values. Represented as 1 (true/high) and 0 (false/low) . It’s the foundation of all digital electronics , from simple gates to full CPUs. Every digital circuit you’ll ever build using 74LS chips, microcontrollers, or even a 6502 ultimately follows Boolean rules. Think of Boolean logic as mathematics for truth,  where instead of adding numbers, we combine logical conditions. The Basic Boolean Operators These three operators form the basis of Boolean algebra . Every logic gate, circuit, and even program condition can be expressed using these symbols. Truth Tables A truth table lists all possible combinations of inputs and the resulting output. They’re one of the most useful tools when designing or testing...

Building a Full Adder, Combining Logic to Add Three Bits When you add two binary digits, a half adder is enough. But what if there’s already a carry bit from a previous addition? That’s where the full adder comes in. It’s the next logical step in building real digital circuits, from binary adders to full ALUs in CPUs. What a Full Adder Does A full adder adds three input bits : A B Carry In (Cin) and gives two outputs: Sum (S) – the result of the bit addition Carry Out (Cout) – the overflow bit for the next stage Logic Design You can think of a full adder as two half adders plus an OR gate . First half adder adds A and B which produces an intermediate Sum₁ and Carry₁ Second half adder adds Sum₁ and Cin which produces final Sum and Carry₂ OR gate combines Carry₁ and Carry₂ which gives Carry Out Equations:      Sum = A ⊕ B ⊕ Cin      Carry_out = (A · B) + (Cin · (A ⊕ B)) Components You’ll Need 1 × 74LS86 ( XO...

Understanding the Real Electronics Behind Logic Gates (The Practical Math Behind Digital Circuits) When we build circuits with logic chips like the 74LS series, it’s easy to think only in 1s and 0s. But under the hood, every logic gate follows the same rules as any other circuit, Ohm’s Law, current limits, and voltage thresholds. So yes, there is real-world math behind those blinking LEDs and logic tables.  1. Logic Levels — The Digital View At the logic level, everything is simple: 0 V → LOW (logic 0) 5 V → HIGH (logic 1) We don’t care about exact voltages here just whether a signal crosses a defined threshold. For TTL (Transistor-Transistor Logic) chips like the 74LS86 XOR gate , these thresholds are: This means a logic gate “decides” based on whether the voltage is above or below that boundary, which is how binary logic becomes real voltage levels. 2. Inside the Circuit — Real Electrical Math Even though logic circuits process bits, they still obey Ohm’s Law ...

  Building a Half Adder – Combining Logic Gates A Half Adder is one of the simplest examples of how digital logic gates can be combined to perform arithmetic. It takes two binary inputs and outputs their sum and carry,  just like how you’d add two 1-bit numbers on paper. If you’ve already built your AND , OR , and XOR gate projects, this is where things start getting interesting, we’ll combine them into a working digital circuit. What You’ll Learn How a half adder performs binary addition How to combine an XOR and an AND gate How to test and visualize binary outputs with LEDs Understanding the Logic When you add two binary digits (A and B), the possible outcomes are: Here’s what’s happening: Sum is A XOR B → only true when one input is HIGH. Carry is A AND B → only true when both inputs are HIGH. That’s it a Half Adder is literally just an XOR gate and an AND gate working together. Parts You’ll Need 1 × 74LS86 (XOR gate) 1 × 74LS08 ...