Logic Circuits and D-Type Flip-Flops

Overview

Recall questions on interpreting logic circuits, completing truth tables, drawing circuits for Boolean expressions, and what the edge-triggered D-type flip-flop is, how it is drawn and what it stores.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Interpret this circuit: inputs A and B go into an AND gate; the output of that AND gate and input C go into an OR gate, whose output is Q. Write the Boolean expression.

   Model answer

   Q = (A AND B) OR C, written in symbols as Q = A.B + C. Work outwards from the inputs: the AND gate produces A.B, and that signal is then one of the two inputs of the OR gate along with C.

2. 2

   Consider this circuit. Inputs A, B and C. A and B go into an AND gate. C goes into a NOT gate. The outputs of the AND gate and the NOT gate go into an OR gate, whose output is Q. Write the Boolean expression for Q.

   Model answer

   Q = (A AND B) OR (NOT C), written in symbols as Q = A.B + NOT C.

3. 3

   Complete the truth table for Q = (A AND B) OR (NOT C), taking the rows in the order 000 to 111.

   Model answer

   Listing A, B, C then the intermediate values A.B and NOT C, then Q: 0,0,0 gives 0 and 1, so Q = 1. 0,0,1 gives 0 and 0, so Q = 0. 0,1,0 gives 0 and 1, so Q = 1. 0,1,1 gives 0 and 0, so Q = 0. 1,0,0 gives 0 and 1, so Q = 1. 1,0,1 gives 0 and 0, so Q = 0. 1,1,0 gives 1 and 1, so Q = 1. 1,1,1 gives 1 and 0, so Q = 1. The output column reading down is 1,0,1,0,1,0,1,1.

4. 4

   What is the reliable method for completing a truth table for a circuit you have not seen before?

   Model answer

   First count the inputs: with n inputs there are 2 to the power n rows, and you write the input combinations in binary counting order so none is missed. Then add one extra column for the output of each intermediate gate, in the order the signals flow through the circuit, and fill those columns one gate at a time using only the columns to their left. The final column is the output of the last gate. Never try to evaluate a whole circuit in your head in one step.

5. 5

   Draw an equivalent logic gate circuit for the Boolean expression Q = (A XOR B) AND (NOT C).

   Model answer

   Three input lines A, B and C on the left. A and B go into the two inputs of an XOR gate. C goes into a NOT gate. The output of the XOR gate and the output of the NOT gate are the two inputs of an AND gate, and the output of that AND gate is Q. Build it from the inside of the brackets outwards: each bracket becomes a gate, and the operator joining the brackets becomes the final gate.

6. 6

   Draw an equivalent logic gate circuit for Q = NOT (A OR B) AND A, and say what it does.

   Model answer

   Input A branches: one branch goes to an OR gate, the other goes on to a later AND gate. Input B goes into the second input of the OR gate. The OR gate's output goes into a NOT gate. The outputs of that NOT gate and the branched line A are the two inputs of an AND gate, whose output is Q. The output is always 0: NOT (A OR B) can only be 1 when A is 0, and the AND then requires A to be 1, which is impossible.

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