Question

A NOR gate and a NAND gate are connected as shown in the figure. Two different sets of inputs are given to this set up. In the first case, the input to the gates are A=0,B=0,C=0. In the second case, the inputs are A=1,B=0, C=1. The output D in the first case and second’s case respectively are:

1. 0 and 0
2. 0 and 1
3. 1 and 0
4. 1 and 1

Answer 1

Here there are two gates applied one is NOR and another is NAND. The two gates perform the same logical operation as an OR & AND gate, it is just that the output is reversed in case of NOR and NAND gate. The NOR gate performs addition operation and NAND gate performs multiplication operation.

Complete step by step solution:
Complete the “NOR” & “NAND” operations.
Step 1: First operation at A=0, B=0, C=0.
Apply the NOR & AND operations:

1. A+B = 0+0 = 0;
   2)$\overline {A + B} = 1$;
2. $\overline {A + B}$AND C =$\overline {A + B} \times C = 1 \times 0 = 0$;
3. $\overline {\overline {A + B} \times C} = 1$;
   So, the output for the first input where A=0, B=0, C=0. We get the output as “1”.

Step 2: Second operation at A=1, B=0, C=1.
Apply the NOR & AND operations:

1. A+B = 0+1 = 1;
2. $\overline {A + B} = 0$;
3. $\overline {A + B}$ AND C =$\overline {A + B} \times C = 0 \times 1 = 0$;
4. $\overline {\overline {A + B} \times C} = 1$;
   So, the output for the first input where A=0, B=0, C=0. We get the output as “1”.

Final Answer: Option “4” is correct.. The output D in the first case and second’s case respectively are 1 and 1.

Note: Logic gates such as NOR & NAND are the most basic building blocks of any system that is digital. In these gates there are one or more inputs and only one output. The relation between the input and the output is based on a certain logical frame. For various operations there are various logic gates accordingly.