1. Review the results in the chart form of the four cases for adding 2 binary digits?
Case 1
Through the addition of two binary zeroes: 0+0=0 when two zeros are added the sum is 0 in the binary number system. And you can carry the 0 to the next significant bit.
Case 2
The Addition of 1 and 0: 1+0=1: Through the addition of 1 and 0 the sums are 1 and 0 and this can be carried to the next significant bit.
Case 3
Through the addition of 1 and 0: 0 + 1 = 1. When 0 and 1 are added, the sum is 1 and a 0 is carried to the next significant bit. (In the Binary system)
Case 4
Through the addition of1 and 1: 1 + 1 = 0 and carry 1. In the binary system, when 1 and 1 are added, the sum is 0 and the 1 is carried to the next significant bit.
Case 1
Through the addition of two binary zeroes: 0+0=0 when two zeros are added the sum is 0 in the binary number system. And you can carry the 0 to the next significant bit.
Case 2
The Addition of 1 and 0: 1+0=1: Through the addition of 1 and 0 the sums are 1 and 0 and this can be carried to the next significant bit.
Case 3
Through the addition of 1 and 0: 0 + 1 = 1. When 0 and 1 are added, the sum is 1 and a 0 is carried to the next significant bit. (In the Binary system)
Case 4
Through the addition of1 and 1: 1 + 1 = 0 and carry 1. In the binary system, when 1 and 1 are added, the sum is 0 and the 1 is carried to the next significant bit.
2. Compare question 1 with the observations in this experiment.
Comparing question 1 with the observations in this experiment is simple as the results match. Remembering how the output depends on the two Inputs A and Input B and this is exactly like how the carry digits depend on the two numbers that were being added in the binary addition. This basically means that when compared both would have the same truth table. Also when looking at question 1 you can also see that the sum digits are the same as the OR gat truth table and the carry digits are exactly the same to the AND gate (that is why this is called a binary addition, so this lab was basically an addition of two gates.)
3. When two digits are added, a sum and a carry are obtained. For example when 1 + 0 are added the sum is 1 and the carry is 0. How should the LED outputs in this experiment be interpreted?
As for this experiment there are two LED outputs. Therefore output 1 and LED 1 should be understood as the same output value as the sum digit of two binary numbers that are being added or two inputs. Whereas LED 2 should be interpreted as the same output value as the carry digit of the binary numbers that are being added or inputs A and B. An example would be if two digits were high (1+1) the sum of this would be 0 LED will be off as output 1 is the sum digit. But the carry when both inputs are high (1+1) is 0. Therefore, LED 2 will be high or will turn on because output 2 corresponds to the carry digit. The four cases for adding two binary digits can be used to interpret the LED outputs in this experiment.
4. When any 2 numbers with more than 1 digit per number are added, the addition at any place value requires the addition of 2 digits from the present value plus the carry from the previous place value. For example:
CASE A CASE B
B A 1. Add digits: (1 + 0)
1 1 2. Result:
0 1 Sum = 1, Carry = 0
1 0 0 3. Add sum and carry from Case A (1 + 1)
4. Result:
Sum = 0, Carry 1
Our circuit will stimulate Case A. Describe a circuit that stimulates Case B?
The following is the truth table that correlates to the given circuit:
As for this experiment there are two LED outputs. Therefore output 1 and LED 1 should be understood as the same output value as the sum digit of two binary numbers that are being added or two inputs. Whereas LED 2 should be interpreted as the same output value as the carry digit of the binary numbers that are being added or inputs A and B. An example would be if two digits were high (1+1) the sum of this would be 0 LED will be off as output 1 is the sum digit. But the carry when both inputs are high (1+1) is 0. Therefore, LED 2 will be high or will turn on because output 2 corresponds to the carry digit. The four cases for adding two binary digits can be used to interpret the LED outputs in this experiment.
4. When any 2 numbers with more than 1 digit per number are added, the addition at any place value requires the addition of 2 digits from the present value plus the carry from the previous place value. For example:
CASE A CASE B
B A 1. Add digits: (1 + 0)
1 1 2. Result:
0 1 Sum = 1, Carry = 0
1 0 0 3. Add sum and carry from Case A (1 + 1)
4. Result:
Sum = 0, Carry 1
Our circuit will stimulate Case A. Describe a circuit that stimulates Case B?
The following is the truth table that correlates to the given circuit:
An Exclusive OR Gate (provided by the integrated circuit 7486) and an AND Gate (provided by the integrated circuit 7408) simulates the required circuit.The truth table for the circuit above is similar to the circuit in this lab. The XOR gate produces the binary sum of the two inputs while the AND gate produces the carry of the outputs.