---
title: "Logic Circuits That Add and Remember"
description: "The half adder and full adder that turn gates into binary arithmetic with a carry, and the flip-flop that holds one bit after its input has gone. Feedback is what turns a circuit into storage."
canonical: https://lightmysky.com/learn/computing/logic-circuits-that-add-and-remember-mt_zPgkt6zf-i
source: https://lightmysky.com/learn/computing/logic-circuits-that-add-and-remember-mt_zPgkt6zf-i.md
retrieved: 2026-09-12
---

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# Logic Circuits That Add and Remember

The half adder and full adder that turn gates into binary arithmetic with a carry, and the flip-flop that holds one bit after its input has gone. Feedback is what turns a circuit into storage.

Subject: Computing · Area: Computer Systems · Ages 16 to 17
Page: https://lightmysky.com/learn/computing/logic-circuits-that-add-and-remember-mt_zPgkt6zf-i

## Ready when they can

- Give the sum and carry a full adder produces for each combination of its three inputs
- Chain full adders to add two four-bit numbers and show where overflow appears
- Explain what a flip-flop holds and why feedback is needed to hold it

## Lesson: Circuits that add and remember

Gates alone only decide, but wired together they can calculate. A half adder adds two bits and reports two answers: the sum bit and the carry bit. Adding 1 and 1 gives sum 0 with carry 1, exactly like carrying into the next column on paper.

**Example.** A full adder handles one column completely: it adds the two column bits plus the carry in from the column before. Feeding 1, 1 and carry in 1 gives sum 1 with carry out 1, since three ones make binary 11. Chain four full adders and each carry out becomes the next carry in, rippling left.

A carry out of the leftmost column has nowhere to go, and that is overflow. Adding 1011 and 0110 gives sum bits 0001 with a final carry of 1, so the true answer needs five bits and a four bit box overflows. No final carry means the answer fits.

**Tip.** A flip-flop is the part that remembers: it holds one bit by feeding its output back to its input. Without that feedback loop, a circuit output only mirrors its present input, so the bit vanishes the moment the input changes.

**Recap.** Adders total each column with carries, overflow is the homeless final carry, and feedback is what holds a bit.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Boolean Algebra and Simplifying Logic Expressions](https://lightmysky.com/learn/computing/boolean-algebra-and-simplifying-logic-expressions-mt_9MrE1N63D5)
- [Adding Binary Numbers and Overflow](https://lightmysky.com/learn/computing/adding-binary-numbers-and-overflow-mt_dBS2OoQscq)

## Opens up

- [Assembly Language and the Instruction Set](https://lightmysky.com/learn/computing/assembly-language-and-the-instruction-set-mt_bzmsfvdzwp)
- [Finite State Machines and What They Recognise](https://lightmysky.com/learn/computing/finite-state-machines-and-what-they-recognise-mt_gIk7tQ229w)