Adder fundamentals: Name the two basic adder building blocks used in digital circuits.

Introduction / Context:
Adders are foundational to arithmetic units, counters, checksum generators, and digital signal processing blocks. Understanding the elemental adder cells clarifies how wider adders and ALUs are constructed.

Given Data / Assumptions:

• We seek the canonical names of the smallest adder units.
• System uses binary arithmetic with carry handling.

Concept / Approach:
A half adder adds two single-bit operands and produces a sum and a carry (no carry-in). A full adder extends this by including a carry-in input, allowing chaining to create multi-bit ripple or look-ahead adders. Parallel adders are assemblies of full adders; they are not a different “basic type.”

Step-by-Step Solution:

Verification / Alternative check:
Standard logic libraries and textbooks specify these two as primitive adder cells; all larger adders decompose to these functions.

Why Other Options Are Wrong:

• half adder and parallel adder: “Parallel adder” is a composition of full adders, not a primitive.
• asynchronous and synchronous: Timing classifications, not adder cell types.
• one’s complement and two’s complement: Number representations, not adder circuit types.

Common Pitfalls:
Confusing architectural composition (“parallel adder”) with primitive cells; conflating numeric representations with hardware blocks.

Final Answer:
half adder and full adder