1. Very Large Scale Integrated chips (VLSI) The complexity of the digital computation chips is increasing in line with Moore’s law.The complexity of the digital computation chips is increasing in line with Moore’s law. P6 (Pentium III family) architecture had 5-10 million transistorsP6 (Pentium III family) architecture had 5-10 million transistors Willamette (Pentium4) has 38 million transistorsWillamette (Pentium4) has 38 million transistors It is common today to have over a million transistors.It is common today to have over a million transistors.

2. Cost of errors in ICs The requirements of most ICs do not allow for errors in the design/manufactureThe requirements of most ICs do not allow for errors in the design/manufacture The cost of discovering design bugs increases exponentially after the product is shipped.The cost of discovering design bugs increases exponentially after the product is shipped. The infamous Pentium bug cost intel $475 million in 1993.The infamous Pentium bug cost intel $475 million in 1993.

3. How can errors be found BEFORE building the chip? Simulation! Stimulate (apply input vectors) and then propagate the values through the circuit and observe the output values.Stimulate (apply input vectors) and then propagate the values through the circuit and observe the output values. Equivalence checking:Equivalence checking: –Stimulate (apply input vectors) to 2 circuits, one of them called the known_correct_circuit and the other is the under_test_circuit –check if the output matches when both of the above circuits are applied the same input vector

4. Logic simulation inputsinputs 1 00000000 outputsoutputs 00010001 00100010 11111111 0111

5. Different kinds of digital circuits Combinational circuit with n input bits and m output bits with no don’t cares or properties on the inputs (all 2 n bit combinations are valid inputs to the circuit)Combinational circuit with n input bits and m output bits with no don’t cares or properties on the inputs (all 2 n bit combinations are valid inputs to the circuit) Combinational circuit with n input bits and m output bitsCombinational circuit with n input bits and m output bits Sequential circuits: have definite set of input bit vectors for each “test”.Sequential circuits: have definite set of input bit vectors for each “test”.

6. Encoding of the function table of a circuit into Ptrees Bit1Bit2SumCarry 0000 0110 1010 1101 Function table of a half adder circuit

7. Function table of a Full adder circuit input1input2 Carry forward Sum 0000 0011 0101 0110 1001 1010 1100 1111Carry0 0 0 1 0 1 1 1