Building a Full Adder

Build a full adder using XOR, AND, and OR gates—adds three bits including a carry input, enabling multi-bit arithmetic.

Overview

A full adder extends the half adder by accepting a carry input from a previous stage. This allows full adders to be chained together for multi-bit addition. The circuit uses two XOR gates, two AND gates, and one OR gate to add three single bits (A, B, and Carry-in) and produce a sum and carry-out.

Components Needed

  • 1x SN74HC86 IC (XOR)
  • 1x CD4081 IC (AND)
  • 1x SN74LS32 IC (OR)
  • 2x LED
  • 3x Switch
  • severalx Wires

Instructions

  1. Gather Your Components

    You'll need three ICs: SN74HC86 (XOR), CD4081 (AND), and SN74LS32 (OR). Also gather three switches, two LEDs, wires, breadboard, and 5V power source.

  2. Wire the Full Adder Circuit

    Place all three ICs on the breadboard and power them. Connect switches A and B to the first XOR and AND gates. The XOR output feeds a second XOR gate along with switch C (carry-in), producing Sum. For Carry-out, OR together: (A AND B) with ((A XOR B) AND Cin).

  3. Test: 000 → Sum=0, Carry=0

    All switches OFF (A=0, B=0, Cin=0). Adding 0+0+0=0. Both LEDs should be OFF.

  4. Test: 100 → Sum=1, Carry=0

    A ON, B and Cin OFF (A=1, B=0, Cin=0). Adding 1+0+0=1. Sum LED ON, Carry OFF.

  5. Test: 010 → Sum=1, Carry=0

    B ON, A and Cin OFF (A=0, B=1, Cin=0). Adding 0+1+0=1. Same result: Sum ON, Carry OFF.

  6. Test: 001 → Sum=1, Carry=0

    Cin ON, A and B OFF (A=0, B=0, Cin=1). Adding 0+0+1=1. The carry-in passes through as the sum.

  7. Test: 110 → Sum=0, Carry=1

    A and B ON, Cin OFF (A=1, B=1, Cin=0). Adding 1+1+0=10 binary. Sum=0, Carry=1.

  8. Test: 011 → Sum=0, Carry=1

    B and Cin ON, A OFF (A=0, B=1, Cin=1). Adding 0+1+1=10 binary. Sum=0, Carry=1.

  9. Test: 101 → Sum=0, Carry=1

    A and Cin ON, B OFF (A=1, B=0, Cin=1). Adding 1+0+1=10 binary. Sum=0, Carry=1.

  10. Test: 111 → Sum=1, Carry=1

    All switches ON (A=1, B=1, Cin=1). Adding 1+1+1=11 binary (3 decimal). Both LEDs ON!

Challenges

  • Chain multiple full adders to build a 4-bit adder (next project!)
  • Add an overflow detection output for signed number addition
  • Build a subtractor by inverting one input and setting Cin=1 (two's complement)
  • Compare propagation delay with a dedicated adder IC like 74LS83