Sample questions from Boolean Algebra

Answer each one closed book first, then open the answer.

1. Logic Gates and Truth Tables

   Describe the NAND gate and give its truth table.

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   The symbol is the AND gate's D shape with a small circle on its output, the circle indicating inversion. It is NOT AND, so its output is the exact opposite of AND: 1 in every case except when all inputs are 1. Truth table: 0,0 gives 1; 0,1 gives 1; 1,0 gives 1; 1,1 gives 0.

2. Logic Gates and Truth Tables

   What happens if you connect both inputs of a NAND gate to the same signal? Work it out from the truth table.

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   Only two rows are then reachable. With both inputs 0, NAND gives 1; with both inputs 1, NAND gives 0. That is exactly the behaviour of a NOT gate, so a NAND with its inputs tied together inverts. The same trick works with a NOR gate, whose 0,0 row gives 1 and 1,1 row gives 0.

3. Defining Problems Using Boolean Logic

   Write an expression, in terms of A and B only, that is true when exactly one of the two inputs is true, without using the XOR symbol.

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   Q = A.B' + A'.B - that is, A true and B false, or A false and B true. This is the sum-of-products form of exclusive OR, and it is exactly what an XOR gate does. Writing it out this way is useful when you need to build the function from AND, OR and NOT gates only.

4. Boolean Algebra Rules and Simplification

   Simplify NOT(A AND B) OR A.

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   Apply De Morgan's first law to the bracket: (A.B)' = A' + B'. The expression becomes A' + B' + A. Commuting and regrouping gives (A + A') + B'. Since A + A' = 1 and 1 OR anything is 1, the whole expression simplifies to 1 - it is always true, whatever A and B are, so the circuit could be replaced by a permanent logic 1.

5. Boolean Algebra Rules and Simplification

   What does the symbol ≡ mean in a Boolean expression?

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   It means equivalence: A ≡ B is true when A and B have the same truth value, both true or both false.

6. Half Adders, Full Adders and D-type Flip Flops

   Give the truth table for a half adder.

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   Inputs A and B, outputs sum S and carry C. A=0, B=0 gives S=0, C=0. A=0, B=1 gives S=1, C=0. A=1, B=0 gives S=1, C=0. A=1, B=1 gives S=0, C=1, because 1 + 1 in binary is 10, so the sum digit is 0 and 1 is carried.

The 5 subtopics

One subtopic is one session. Work down the list.

How the guide is worked

Answering a question from memory stores it far better than reading the answer again. The guide runs that as a fixed procedure on one subtopic at a time, about twenty minutes a session.

1. Step 1 · Closed book

   Cover the answers. Work through one subtopic and write down what you can. Leave blanks where you have nothing.

2. Step 2 · Open book

   Go back to the top. Read each printed answer and write it out in full, including the ones you had right.

3. Step 3 · Closed book again

   Same questions, same order, from memory. The gap between pass one and pass three is the session result.

Read the full method, the return schedule and the research behind it.

Nearby topics

All 16 topics · Guide overview