1. (a) By using a truth table show that the expressions

are equivalent.

(b) Show by plotting truth tables that

2. (a) Draw the logic circuit to represent the following Boolean expression using only NAND gates.

(b) Draw the logic circuit to represent the following Boolean expression using only NOR gates.

Indicate the outputs of each gate.

3. In the ladder diagram shown in FIGURE 1, Y006 is a lamp, X and R references are relay contacts. Write down the Boolean expression for the lamp to light.

4. (a) Add the following HEX numbers converting to binary. Express the answer in HEX.
(i) 08 + 03
(ii) OABC + DAOE.
(b) Write down the 2's complement of:
(i) 00000001
(ii) 00111100
(c) Convert the following denary numbers to 8 bit binary numbers and evaluate using the '2's' complement' method. Leave your answers in binary form.
(i) 17 - 8
(ii) 97 - 125
(d) (i) Write down the bcd form of decimal 845.
(ii) Convert the denary number 818 first to hexadecimal then to binary.
Show all working.

5. State three disadvantages of relays when compared with the use of PLCs in process control circuits.

6. (a) State what is meant by input and output interfaces in relation to PLCs.
(b) State briefly what the function of interfaces is in relation to the different types of process signal.
(c) The diagram of FIGURE 2 shows a bi-directional opto coupler input interface circuit. When a supply voltage of 20 V is applied the LED carries a current and 2 V is dropped across it. Calculate the value of the LED current and the value of current through the 3 kQ resistance.

External wiring Internal wiring

(d) The circuit shown in FIGURE 3 is part of the interface of a relay output module. I_b is 1 mA and V_cc is 9 V. The relay requires a minimum of 50 mA to energise.

Complete the values of the assumptions listed below in order to calculate:
• voltage across R₁
• value of R₁
• voltage across the relay coil
• voltage across R₂
• value of R₂
• collector of current I_c
Assumptions:
Logic '1' = V
Logic '0' = V
Transistor forward current gain h_fc =
LED current = 10 mA
LED voltage drop at 10 mA = V
Base/emitter voltage = V
Collector emitter voltage when transistor is on = 1 V