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.