Ripple Carry Critical Path Analysis
Arithmetic circuits dictate the maximum clock frequency of an entire chip. The ripple carry adder represents the most fundamental approach to multi-bit addition, cascading single-bit full adders to compute wider results.
A 4-bit ripple carry adder consists of four cascaded full adders. Each full adder computes Sum = A XOR B XOR Cin and Cout = (A AND B) OR (Cin AND (A XOR B)). The inputs are A[3:0], B[3:0], and an initial carry-in Cin. The outputs are S[3:0] and Cout. All 2-input logic gates (AND, OR, XOR) have an equal propagation delay of 1 unit.
Trace the signal propagation through the cascaded stages. Identify the critical path through this combinational logic chain and determine the worst-case gate delay from the arrival of inputs to the stabilization of the final outputs.
Constraints
- Assume all input signals arrive simultaneously at time t=0.
- Assume all 2-input gates (AND, OR, XOR) have a delay of exactly 1 gate unit.
- Fan-out delay effects are ignored.
Topics
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