PYTHON · NUMPY

The Adder

Compose gates into a full adder, then chain them into an 8-bit ripple-carry adder that actually adds.

01Challenge

Wire your gates into a 1-bit full adder (sum + carry), then chain eight of them so the carry ripples through. It must add any two 8-bit numbers correctly, carry and all.

02Model

Arithmetic is just logic arranged with intent. A full adder takes two bits plus a carry-in and produces a sum bit and a carry-out: sum is the XOR of all three; carry-out is true when at least two inputs are. Chain N of them, carry-out feeding the next carry-in, and you have an N-bit adder — the ripple-carry adder, the first real datapath. Every processor's ALU begins here.

03Guided practice

Worked: build XOR from your gates. Faded: write full_adder(a,b,cin) → (sum,cout). Independent: ripple eight of them and test against ordinary addition.

04Feedback

PASS WHEN Your ripple-carry adder matches real addition across the full 8-bit range — a datapath, from first principles.

If your run fails, check:

FAIL: sums wrong — the sum bit is XOR(XOR(a,b),cin); re-check your XOR.
FAIL: carry wrong — carry-out is true when any two of a, b, cin are 1.

05Retrieve & space

What are a full adder's two outputs? (Sum = XOR of all three inputs; carry-out = majority of the three.)
Why is it called 'ripple'-carry? (Each stage's carry-out feeds the next stage's carry-in, rippling down the chain.)
What real block is this? (The core of a CPU's arithmetic-logic unit.)

06Mastery & project

Composes a full adder from gates and chains an N-bit ripple-carry adder verified against integer addition (L2: build a correct datapath from primitives).

The adder is the arithmetic your Module-3 multiply-accumulate unit is built on.

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PYTHON · NUMPY

The Adder

Build a full adder from gates, ripple eight, and verify against real addition.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you