Adder Circuits — Half Adders, Full Adders & Ripple Carry
Learn how logic gates are combined to build half adders, full adders, and ripple-carry adders for binary addition.
📚 Learning Steps
💡 Study Tips
- • Read through at your own pace
- • Try the interactive simulators hands-on
- • Study the pseudocode — it appears in exams
- • Quiz yourself before moving on
Step 1: Why Do We Need Adder Circuits?
📖 TheoryAt the hardware level, a computer's ALU (Arithmetic Logic Unit) needs to add binary numbers together. But the ALU is built from logic gates — AND, OR, NOT, XOR.
So how do we add using only logic gates?
Recall binary addition rules:
•0 + 0 = 0 (sum=0, carry=0)
•0 + 1 = 1 (sum=1, carry=0)
•1 + 0 = 1 (sum=1, carry=0)
•1 + 1 = 10 (sum=0, carry=1)
Look at the SUM column — it matches XOR!
Look at the CARRY column — it matches AND!
This insight leads directly to the half adder circuit.
🎯 Key Points
- •Computers add binary numbers using logic gate circuits
- •The ALU is built from combinations of AND, OR, NOT, and XOR gates
- •Binary addition of two 1-bit numbers: sum = XOR, carry = AND
- •Half adder → full adder → ripple carry (builds up in complexity)
- •Understanding adders shows how hardware performs arithmetic
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