Explain the SOP based implementation of the Adjacent 1s Detector-00336
This subjective question is related to the book/course
vu cs201 Introduction to Programming.
It can also be found in
vu cs201 Mid Term Solved Past Paper No. 3.
Question 1: Explain the SOP based implementation of the Adjacent 1s Detector Circuit
The total gate count is
Answer:
The Adjacent 1s Detector accepts 4-bit inputs. If two adjacent 1s are detected in the input, the output is set to high. The operation of the Adjacent 1s Detector is represented by the function table. Table 13.6. In the function table, for the input combinations 0011, 0110, 0111, 1011, 1100, 1101, 1110 and 1111 the output function is a 1. Implementing the circuit directly from the function table based on the SOP form requires 8 AND gates for the 8 product terms (minterms) with an 8-input OR gate. Figure 13.3.The total gate count is
- One 8 input OR gate
- Eight 4 input AND gates
- Ten NOT gates
The expression can be simplified using a Karnaugh map, figure 13.4, and then the simplified expression can be implemented to reduce the gate count. The simplified expression is AB + CD +BC . The circuit implemented using the expression AB + CD +BC has reduced to 3 input OR gate and 2 input AND gates.
The simplified Adjacent 1s Detector circuit uses only four gates reducing the cost, The size of the circuit and the power requirement. The propagation delay of the circuit is of the order of two gates.
