Half Adder Circuit Tracer

About this interactive

What you're seeing: the finished half adder from the lesson video, drawn the way the video draws it. Two inputs run along the top and feed both an AND gate on the left and an OR gate on the right. The AND gate's output is the Carry; it also feeds a NOT gate hanging underneath it. The OR gate's output, which the video calls X, and the NOT gate's output both feed a second AND gate at the bottom right, and that gate's output is the Output bit. Beside the circuit is the half adder's truth table, with columns Input 1, Input 2, Output and Carry, and a readout that writes the current inputs as a binary addition, for example 1 + 1 = 10. Why it matters: the video builds this circuit one gate at a time, and a student who watched it has seen the answer without necessarily being able to check it. The truth table only shows what goes in and what comes out; the reasoning lives on the two wires in the middle. So every wire here carries its bit on screen, the same way the video annotates each wire with a hand-written 0 or 1. X reads 0 1 1 1 down the table, which is almost the Output column but wrong for 1 + 1. NOT carry reads 1 1 1 0, which is off in exactly that one row. The final AND of the two gives 0 1 1 0. Watching those two intermediate values change is what turns the circuit from something to memorize into something you can reason your way through. How to use it: before you flip a switch, predict what every gate will output, then check yourself against the lit wires. Click a truth-table row to jump to its inputs, and save 1 + 1 for last, the one case where the carry turns on and the Output turns off.

How to use this tool

This is the half adder from the video, finished and live. It adds two single bits: Input 1 and Input 2 go in, and Output (the sum bit) and Carry come out.

Flip the Input 1 and Input 2 switches, or click a row of the truth table to jump straight to that row's inputs.
A wire carrying 1 lights up; a wire carrying 0 stays dim. The small yellow number on each wire is the bit it carries right now, including the two wires in the middle: X (the OR gate's output) and NOT carry.
The highlighted row of the truth table always matches the switches.

Predict before you flip. Each time, say what all four gates will output first, then check yourself against the wires.

Trace it the way the video built it:

Carry is an AND. You only carry when both bits are 1, which is exactly when an AND gate outputs 1.
OR gets you close. Down the table, X reads 0 1 1 1. The Output column needs 0 1 1 0, so OR is right in every row except 1 + 1.
NOT flips the carry. NOT carry is 1 in every row except 1 + 1, the one row where X is wrong.
The last AND combines them. While NOT carry is 1 it lets X straight through; when the carry is 1 it switches Output off. That turns 0 1 1 1 into 0 1 1 0.

Save 1 + 1 for last: watch the carry light up, NOT carry go dark, and Output switch off. 1 + 1 = 10 in binary, so the 1 goes to the carry and the Output is 0.

Nothing here is graded.

What you'll learn

Trace the bit on every wire of a half adder for any pair of inputs, including the OR output and the inverted carry in the middle of the circuit
Explain why the carry bit is a single AND of the two inputs, and why the Output bit needs an OR, a NOT and a second AND working together
Connect each row of the half adder's truth table to single-bit binary addition, including why 1 + 1 gives an Output of 0 and a Carry of 1

Aligned to

CompTIA Tech+

1.3 Illustrate the basics of computing and processing.

Key terms

Half Adder: A combinational circuit built from AND and OR/NOT gates that adds two single-bit binary numbers and produces a Sum output and a Carry output.
Carry Output: The overflow bit produced by a half adder when the addition of two binary digits exceeds the value representable in a single bit, passing a 1 to the next column.
Sum Output: The result bit of a half adder that represents the least-significant bit of adding two binary digits together.
AND Gate: A logic gate that outputs 1 only when all inputs are 1; outputs 0 in all other cases.
OR Gate: A logic gate that outputs 1 when at least one input is 1; outputs 0 only when all inputs are 0.
NOT Gate: A logic gate that inverts its single input, outputting 1 when the input is 0 and 0 when the input is 1.
Truth Table: A table that lists all possible input combinations for a logic gate and their corresponding output values.
Binary Addition: The arithmetic process of adding two binary numbers using base-2 rules, where 0+0=0, 0+1=1, 1+1=10 (sum 0 carry 1), and 1+1+1=11 (sum 1 carry 1).
Logic Gate: A basic electronic circuit that performs a Boolean operation on one or more binary inputs to produce a single binary output.
Bit: Short for binary digit, the smallest unit of data in computing, holding a single value of 0 or 1; all digital information is ultimately composed of bits.

Topics

Half Adder Logic Gates Binary Addition Truth Tables Digital Logic Binary Circuits Carry

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