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A Useful Binary Computer: The Full Adder and a 4-Bit Adder

Your half adder can add two bits. That's a start, but real numbers have more than one digit. In this lab you'll build an adder that can pass a carry from one column to the next, then chain four of them into a circuit that adds real binary numbers — the arithmetic heart of a computer.

Overview

You'll build a full adder from two half adders and an OR gate, then chain four full adders into a 4-bit adder and test it, including the case where the answer is too big to fit — overflow.

Before you start

Open Antares with your HA (half adder) and MyOR gate available.

You've got it when…

  • Your full adder gives the correct SUM and Cout for all eight input combinations.
  • Your 4-bit adder correctly adds two 4-bit numbers.
  • You can show it handling a no-carry sum, a sum with carry, and an overflow.

Collaboration & AI

Work: On your own. A neighbor can help you untangle wires; the design is yours.

AI — AIAS Level 1, No AI: Build and test the adder yourself. What the levels mean.

The Plan

Your half adder gives you a Sum and a Carry (which shows the sum overflowed into the next column). A full adder does the same, but it also accepts a carry-in from a previous addition.

  • Half adder — adds 2 bits (no carry-in).
  • Full adder — adds 3 bits (two inputs plus a carry-in).

Today you'll build a full adder that handles one column plus a carry-in, then chain them to add multi-digit binary numbers.

Building the Full Adder

Complete the truth table for the full adder based on the description above.

Full Adder

A B Cin (carry-in) SUM (A+B+Cin) Cout (carry-out)
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

Follow these steps to build it:

  1. Create a new circuit named FA (full adder).
  2. Add three Circuit Inputs and rename them Cin, A, and B.
  3. Insert two of your HA (half adder) components.
  4. Insert your MyOR gate.
  5. Add two Circuit Outputs and rename them SUM and Cout.
  6. Arrange and connect the components as shown below.
  7. Test the full adder in simulation for every row of the truth table.

The full adder built from two half adders and a MyOR gate.

Building a 4-Bit Adder

Now that you have a full adder — a component that adds two bits plus a carry-in — you can build a circuit that adds multi-bit binary numbers. We'll add two 4-bit numbers.

  1. Create a new circuit named 4-bit Adder.

  2. Add 8 Circuit Inputs and 4 Circuit Outputs. Rename and arrange them as shown, leaving room between the rows for wiring. Use the Text tool for the plus sign and the Polyline tool for the line.

    Inputs A3–A0 and B3–B0 and outputs S3–S0 laid out with a plus sign.

  3. Add four of your FA components in a vertical row to the right, with some space between them.

    Four full-adder components stacked in a vertical column.

  4. Starting from the top, connect the carry-out of each full adder to the carry-in of the next.

    The four full adders with each carry-out wired to the next carry-in.

  5. Connect each A input to the A input of a full adder.

    Warning

    These must be in order — A0 to the topmost full adder. Take your time and tidy your wires.

    The A inputs wired in order to the full adders.

  6. Do the same with the B inputs.

    Warning

    Again, in order — B0 to the topmost full adder.

    The B inputs wired in order to the full adders.

  7. Connect the sum (S) outputs to the FA SUM outputs the same way — S0 to the topmost full adder.

    The sum outputs wired in order from the full adders.

  8. There is never a carry-in to the first full adder. Connect its carry-in to Ground (from the Net folder) to hold it at zero.

    The first full adder's carry-in tied to ground.

  9. Add a final Circuit Output named Cout to the carry-out of the last full adder. It signals when a sum is too big for 4 bits.

Your finished circuit should look like this.

The completed 4-bit ripple-carry adder with all inputs, outputs, and carry chain wired.

Turn It In

Develop a test plan and submit one screenshot of your simulation for each of these conditions:

  • Two numbers where no digit requires a carry.
  • Two numbers where at least one digit requires a carry.
  • Two numbers whose sum is too large for 4 bits (overflow).

How It's Graded

This lab is worth up to 4 points. One score covers everything you turn in.

Score What it looks like
4 — Excellent The full adder matches all eight rows of its truth table, the 4-bit adder adds correctly, and your three test screenshots genuinely exercise all three conditions — with the binary sums you expected written in your notebook so the evidence checks itself.
3 — Above Average Both circuits work and all three tests are submitted, with a minor gap — a test case that doesn't quite isolate its condition, or one truth-table row wrong.
2 — Average The full adder works but the 4-bit adder has a wiring fault (crossed input order, missing ground on the first carry-in), or tests cover only some of the three conditions.
1 — Below Average The full adder doesn't match its truth table, or the 4-bit adder was not attempted, or no test evidence was submitted.
0 — Failing Nothing turned in, or no evidence of either circuit.