**1.****a) Truth table (Table 1) for a Four-Input digital system is shown below.**

Table 1

i. Using the variable A to represent the 20 digital input, B for 21, C for 22, and D for 23 identify all the possible combinations that produce an even number.

ii. Write down a Boolean expression that will output a HIGH (1) whenever the 4-bit binary input is an even number from Table 1.

iii. Simplify all the above expressions into its simplest form by using a Karnaugh map.

iv. Draw the logic circuit diagram that could be used to represent the simplified Boolean expression in (iii).

**b) Given a combinational logic circuit shown in Figure Q1b below:-**

i. Derive the equation that will produce the output waveform at Z.

ii. Using Boolean algebra, simplify the equation in (i).

iii. Draw the logic circuit for this simplified equation.

iv. Complete the timing diagram Z for the combinational logic

circuit shown in Figure Q1b.

**2.**

a) The logic circuit shown in Figure Q2a is implemented to produce an output at X based on the input conditions at A, B, C and D.

i. Derive the Boolean equation at X.

ii. Use De Morgan’s theorem and then Boolean algebra to simplify the Boolean equation.

iii. Draw the simplified logic circuit.

b) Figure Q2b shows a network of three DC supplies and three resistances. I3 is known to equal 1.5 A. Find the value of I1, I2 and unknown resistance, R.

**Find the following values of**

i. I1

ii. I2

iii. unknown resistance, R.

**c) Figure Q2c shows a typical transformer and rectifier circuit.**

i. What is the open circuit output voltage for the following transformer and rectifier circuit if the input voltage across the primary winding is 110V 50Hz and the primary winding has 1000 turns, whilst the secondary winding has 260 turns?

ii. Draw the output waveform and indicate the peak magnitude of the output voltage.