Interactive Logic Lab

11₂ + 01₂: How the Adders Work Together

Follow the same calculation in the circuit and in column addition.

Logic-gate circuit

Lower bit → Half Adder → carry → upper bit → Full Adder

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A half adder connected to a full adder The lower bits 1 and 1 enter a half adder, giving sum 0 and carry 1. The upper bits 1 and 0 plus that carry enter a full adder, giving sum 0 and final carry 1. 1. HALF ADDER · lower (2⁰) column Inputs: A₀ = 1, B₀ = 1 2. FULL ADDER · upper (2¹) column Inputs: A₁ = 1, B₁ = 0, plus carry from below C₁ = 1 → XOR AND 1A₀ 1B₀ 0S₀ 1C₁ XOR AND XOR AND OR 1A₁ 0B₁ 1 0 1 0S₁ 1 C₂ (final carry)

Binary addition

Compute from right to left, one bit position at a time.

2
4s2s1s
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011 +AB001
?
?
?
11₂ + 01₂ = ?
Start with the rightmost bits

Select Start to trace the two adder circuits and the matching column addition.

ABCarryResultOther values