Cascading adders: result of two 4-bit blocks If you cascade two standard 4-bit binary adders (properly connecting carry-out to carry-in), what width of a parallel adder can you construct?

Introduction / Context:Modular design allows wider arithmetic units to be built from smaller ICs. A classic example is using two 4-bit adder ICs (such as 74xx83) with the carry chain properly linked to realize an 8-bit adder. Understanding cascading is fundamental to building scalable datapaths.

Given Data / Assumptions:

• Each IC implements a 4-bit parallel adder with carry-in and carry-out.
• Carry-out of the lower nibble feeds carry-in of the upper nibble.
• Inputs and sums are arranged to form a continuous 8-bit addition.

Concept / Approach:Parallel adders add all bits of each operand simultaneously, with the carries rippling from least significant to most significant positions. By chaining two 4-bit blocks, you extend the operand width to 8 bits, preserving the same arithmetic behavior with a longer carry path.

Step-by-Step Solution:

Verification / Alternative check:Timing analysis shows ripple-carry delay accumulates across both devices; this matches expectations for an 8-bit adder built from two 4-bit blocks.

Why Other Options Are Wrong:

Common Pitfalls:Forgetting the carry chain; without CO→CI linkage the upper nibble ignores carries.

Final Answer:8-bit parallel-adder circuit