Design of Complex Wending Machine

1. Design of Complex Wending Machine • Inputs: q (quarter), d (dime) and n (nickel) • Input can be two bit coded input or three bit not coded input • Two bit coded: 00 no coin, 01 nickel, 10 dime, and 11 quarter • Three bit not coded: 001 nickel, 010 dime, and 100 quarter • Suppose, we can ask the coin slot to directly return if we cannot accept an input coin • We do this by issuing a signal return coin (rc) • We also generate an output return nickel (rn) and return dime (rd) • We also generate an output to release product (rp) • States: S00, S05, S10, S15, S20, S25, S30, S35, S40, S45, S50 • Notice the names (they need not be S0, S1….) • We also may have S30’ and S35’ where we return coins (we do not need to return in any other state)

2. S35’ d n q q d d d d S05 S15 S25 S35 S45 q q q n n n n n S00 q d n q n n q S10 S20 S30 S40 S50 d d d q n d S30’ q State Changes in Wending Machine Outputs (rc, rn, rd, rp) = (0, 0, 0, 1) in S40 Outputs (rc, rn, rd, rp) = (0, 1, 0, 1) in S45 Outputs (rc, rn, rd, rp) = (0, 0, 1, 1) in S50 Outputs (rc, rn, rd, rp) = (0, 0, 0, 0) in S00, S05, S10, S15, S20, S25, S30, S35 Outputs (rc, rn, rd, rp) = (1, 0, 0, 0) in S30’ and S35’

3. I0 I1 I2 I3 I4 I5 I6 I7 X Y Z S2 S1 S0 0 1 2 3 4 5 6 7 F Multiplexing and Multiplexer • Multiplexers is a circuits which selects one of many inputs • First let us assume that we have one bit inputs • And we have eight inputs, I0, I1, I2, I3, I4, I5, I6, I7 • We want one of them to be output based on selection signal • We need a 3 bit select input to decide which input goes to output • Note the order of select signals • X is MSB and Z is LSB

4. I0 I1 I2 I3 I4 I5 I6 I7 X Y Z S2 S1 S0 0 1 2 3 4 5 6 7 F Multiplexer Design • We can write a logic equation for output F as follows F = X’ Y’ Z’ I0 + X’ Y’ Z I1 + X’ Y Z’ I2 + X’ Y Z I3 + X Y’ Z’ I5 + X Y’ Z I6 + X Y Z’ I6 + X Y Z I7 • This circuit can be implemented using • 8 four-input AND gates and one OR gates

5. S2 S1 S0 0 1 2 3 4 5 6 7 F Designing with multiplexers • Multiplexers can be directly used to implement as a circuit • Easiest way is to use function input as selection signals • Input to multiplxer is a set of 1s and 0s depending on the function to be implemented • We use a 8 to 1 multiplexer to implement function F • Three select signals are X, Y, and Z, and output is F • Eight inputs to multiplexer are 1 0 1 0 1 1 0 0 • Depending on the input signal • multiplexer will select proper output

6. 0 1 2 3 S1 S0 F Using Multiplexers • Suppose we want to design a rotate circuit • Inputs are i3 i2 i1 i0 • Output is zero, one, two, or three bit rotated output • Rotation can be in left or in right direction • Four sets of outputs are • i3 i2 i1 i0 • i2 i1 i0 i3 • i1 i0 i3 i2 • i0 i3 i2 i1 • Input/Output relations ship is given in the table • We can implement this circuit using four 4 to 1 multiplexers