A half adder can be implemented using an XOR gate and an AND gate. Let's assume that the propagation delay of the XOR gate is 2 × 1.2 ms = 2.4 ms (twice that of the AND/OR gate).
A full adder (FA) is implemented using 2 half adders (HA) and 1 OR gate. Therefore, the propagation delay of a full adder is:
Propagation delay of FA = 2 × Propagation delay of HA + Propagation delay of OR
Propagation delay of FA = 2 × (Propagation delay of XOR + Propagation delay of AND) + Propagation delay of OR
Propagation delay of FA = 2 × (2.4 ms + 1.2 ms) + 1.2 ms = 7.2 ms
A 4-bit ripple carry binary adder is implemented using 4 full adders. The total propagation time of this 4-bit binary adder can be calculated as follows:
Total propagation delay of 4-bit ripple carry binary adder = Propagation delay of 1st full adder + Propagation delay of 2nd full adder + Propagation delay of 3rd full adder + Propagation delay of 4th full adder
Total propagation delay of 4-bit ripple carry binary adder = 4 × Propagation delay of FA
Total propagation delay of 4-bit ripple carry binary adder = 4 × 7.2 ms = 28.8 ms
Therefore, the total propagation time of the 4-bit ripple carry binary adder is 28.8 microseconds (µs).
