Reference no: EM132859037

SEE216 Analogue And Digital Electronics - Deakin University

QUESTION 1

Evaluate the following by using binary arithmetic 2's complement method, and express the results in decimal form (including the sign).

A. 100.625₁₀ - A1. D₁₆
B. -1000.0112 - 13. 7₈

QUESTION 2

F1 = (¯AB¯CD + (AC)D¯)¯

A. Create the truth table for F₁ without simplifying the expression (Hint: Create the truth table for the intermediary terms).

B. Simplify F₁ by using a Karnaugh map created from the truth table produced in Question 2A.

F₂ = AB (B + C¯) + B¯C + AB + AB¯

C. Simplify F2 by using Boolean algebra.

QUESTION 3

Consider the digital circuit show in Figure 1. The initialisation (i.e. when t = 0) is as follows.
• All flip-flops are reset, i.e. all main outputs are LOW and all complementary outputs are HIGH.
• Clock signal starts at LOW.

Also, note that all J and K inputs are HIGH. Draw the waveform timing diagram for the signal A, B, C, D, S0, E, and F for 7 clock cycles.

Figure 1: Digital circuit

QUESTION 4

Consider an automatic die reader machine. The machine will perform a sweeping scan of the top surface of the die as shown in Figure 2. The output of the scanner is the signal F, which is HIGH when it is on top of white surface, and LOW when it is on top of dark surface (i.e. the pips).

A. Please explain the relationship between the number of pips and the scanner output F.

B. By only using the JKFF shown in Figure 3 (you can use multiple) and NAND gates (if needed), design a counter circuit to count the number of pips to be displayed on the digital number display (as shown in Figure 4).

Figure 3: Falling-triggered JKFF with active LOW inputs for SET and CLR

Figure 4: Automatic die reader circuit

QUESTION 5

Once you have designed the die reader, you would like to use that for your board game (tabletop game) machine, shown in Figure 5. This machine receives 6 inputs from two die readers. The output of the machine is the signal G, which will be HIGH when Player 1's roll is higher than Player 2's roll, and LOW otherwise.

A. Noting that we have 6 inputs, create a K-map for the output signal G.
B. Based on the K-map from Part A, create the most simplified Boolean expression for G.
C. Draw the logic circuit (Figure 5) for the board game machine. You may use any logic gates.

Figure 5: Logic circuit for the board game machine