Boolean Algebra (OCR A Level Computer Science): Exam Questions

State the purpose of a D-type flip-flop circuit.

A computer scientist has created the following logic circuit shown in Fig. 6.

Fig 6

Complete the truth table for the logic circuit shown in Fig. 6

All users of a computer system have a unique username and password. The computer system has implemented two-factor authentication so that users must respond to either an email or text message containing a secret code to be able to access the system

Let:

A be a Boolean value for if a user enters a valid username

B be a Boolean value for if a user enters a password that matches their username

C be a Boolean value for if a user is able to respond to an email containing a secret code

D be a Boolean value for if a user is able to respond to a text message containing a secret code

Q be a Boolean value for if entry to the computer system is allowed

Complete the Boolean expression below:

Q ≡ .................................................................................

A Boolean expression for a logic system is shown below:

Q ≡ ¬ (¬ A ∧ ¬ B)

Simplify this Boolean expression so that it does not include any negation.

You must explain which Boolean algebra rule(s) you are using at each step.

The logic circuit above has two inputs (A, B) and two outputs (S, C).

Give the Boolean expressions for the outputs S and C.

Complete the truth table for this logic circuit

Describe how this logic circuit can be adapted to add together two 4-bit binary numbers.

Complete the Karnaugh map below for the Boolean expression (¬ A ∧ ¬ B) ∨ ( A ∧ ¬ B)

Use the Karnaugh map to find a simplified Boolean expression that is equivalent to (¬ A ∧ ¬ B) ∨ ( A ∧ ¬ B)

You should highlight the map as appropriate and write the expression.

Describe the inputs and outputs used by a D-type flip-flop circuit, explaining how the inputs are used to control the outputs.

The following Karnaugh map represents another logic circuit.

Use this Karnaugh map to find the simplified expression for this circuit

You should highlight the map as appropriate and write the expression.

Ben installs burglar alarms. The alarm is made up of a door sensor and a motion sensor. When the alarm is set, the siren will sound if either the door sensor or the motion sensor detect movement.

The alarm also has a test mode setting. When the test mode setting is enabled, an engineer can check the sensors are working without the siren going off.

The inputs to the alarm are as follows

Draw a logic circuit to show the logic that is used in the burglar alarm to determine if the siren goes off.

Simplify the Boolean expression ¬A v ¬B using De Morgan’s First Law

Simplify the Boolean expression ¬(¬B) using double negation.

Simplify the Boolean expression (A v B) ˄ (A v C) using distribution.

A logic circuit is designed to control a safety system using four inputs (A, B, C, D). A completed 4×4 Karnaugh map has 1s only in the four corner cells:

• AB = 00, CD = 00

• AB = 10, CD = 00

• AB = 00, CD = 10

• AB = 10, CD = 10

Determine the simplified Boolean expression for the circuit and evaluate how the wrap-around property of the map contributes to reducing the physical hardware required.