Chapter 1, Problem 1CRP

Determine the output of each of the following circuits, assuming that the upper input is 1 and the lower input is 0 What would be the output when the upper input is 0 and the lower input is 1?

Explanation of Solution

Determine the output of the given circuit.

The stated diagram is shown below,

• To find the output of the circuit when the upper input is 1 and the lower input is 0, the diagram contains one XOR gate and inverter, so the Boolean operation of XOR gate and inverter is shown below:

The Boolean XOR operation is shown in table below,

Input 1	Input 2	Output
0	0	0
0	1	1
1	0	1
1	1	0

• First, 0 is the input of inverter which gives the output of inverter and this output of the inverter is the lower input of XOR gate.

The inverter operation is shown in table below,

Input	output
1	0
0	1

• The lower input 0 is converted to 1 through inverter gate that means the lower input of XOR gate is 1.

The inputs of XOR gate are shown in Figure below,

• To represent the output of XOR gate, convert the input of XOR gate through Boolean operation, when both the inputs of XOR gate is 1, then the output of the XOR gate is 0 by Boolean operation XOR table.

Therefore, the required output of the given circuit is “0”.

Determine the output of the given circuit, when the upper input is 0 and the lower input is 1:

• To find the output of the circuit when the upper input is 0 and the lower input is 1, the diagram contains one XOR gate and inverter:
• First, 1 is the input of inverter which gives the output of the inverter and this output of the inverter is the lower input of XOR gate.
• The lower input 1 is converted to 0 through inverter gate, so the lower input of XOR gate is 0.

The inputs of XOR gate are shown in Figure below,

• To represent the output of XOR gate, convert the input of XOR gate through Boolean operation, when both the inputs of XOR gate is 0, then the output of the XOR gate is 1 by Boolean operation XOR table.

Therefore, the required output of the given circuit is “1”.

Explanation of Solution

Determine the output of the given circuit.

The stated diagram is shown below,

• To find the output of the circuit when the upper input is 1 and the lower input is 0, the diagram contains one OR gate and one AND gate, so the Boolean operation of OR gate and one AND gate is shown below:

The Boolean OR operation is shown in table below,

Input 1	Input 2	output
0	0	0
0	1	1
1	0	1
1	1	1

• First, 1 and 0 are the inputs of OR gate that give the output of the OR gate and this output of OR gate is the upper input of AND gate.

The Boolean AND operation is shown in table below,

Input 1	Input 2	output
0	0	0
0	1	0
1	0	0
1	1	1

The upper input 1 and lower input 0 is converted to 1 through OR gate, so the upper input of AND gate is 1.

The inputs of AND gate are shown in Figure below,

• To represent the output of AND gate, convert the input of AND gate through Boolean operation, when the upper input is 1 and lower input is 0 of AND gate, then the output of the AND gate is 0 by Boolean operation AND table.

Therefore, the required output for the given circuit is “0”.

Determine the output of the given circuit, when the upper input is 0 and the lower input is 1:

• To find the output of the circuit when the upper input is 0 and the lower input is 1, the diagram contains one OR gate and one AND gate:
• First, 0 and 1 is the input of OR gate that gives the output of the OR gate which is the upper input of the AND gate.

The upper input 0 and lower input 1 is converted to 1 through OR gate, so the upper input of AND gate is 1.

The inputs of AND gate are shown in Figure below,

Figure (6)

• To represent the output of AND gate, convert the input of AND gate through Boolean operation, when both the inputs of AND gate is 1 then the output of the AND gate is 1 by Boolean operation AND table.

Therefore, the required output for the given circuit is “1”.

Explanation of Solution

Determine the output of the given circuit:

The stated diagram is shown below,

• To find the output of the circuit when the upper input is 1 and the lower input is 0, the diagram contains two XOR gates, so the Boolean operation of XOR gates as shown below:

The Boolean XOR operation is shown in table below,

Input 1	Input 2	output
0	0	0
0	1	1
1	0	1
1	1	0

• First, 1 and 0 are the inputs of XOR gate that give the output of the first XOR gate which is the lower input of second XOR gate.

The upper input 1 and lower input 0 are converted to 1 through XOR gate, so the lower input of second XOR gate is 1.

The inputs of XOR gate are shown in Figure below,

• To represent the output of XOR gate, convert the input of XOR gate through Boolean operation, when both the inputs of XOR gate become 1, then the output of the XOR gate becomes 0 by Boolean operation XOR table.

Therefore, the required output for the given circuit is “0”.

Determine the output of the given circuit, when the upper input is 0 and the lower input is 1:

• To find the output of the circuit when the upper input is 0 and the lower input is 1, the diagram contains two XOR gates:
• First, 0 and 1 are the inputs of first XOR gate that give the output of the first XOR gate which is the lower input of second XOR gate.

The upper input 1 and lower input 0 are converted to 1 through XOR gate, so the lower input of second XOR gate is 1.

The inputs of XOR gate are shown in Figure below,

• To represent the output of XOR gate, convert the input of XOR gate through Boolean operation, when the upper input is 0 and lower input is 1 of XOR gate, then the output of the XOR gate is 1 by Boolean operation XOR table.

Therefore, the required output for the given circuit is “1”.