Half Adder
A half adder can add two binary numbers without a carry. An half adder is a type of “Ripple Carry Adder”. The output of a half adder is sum and carry. Half adder takes in two distinct binary numbers. It cannot work with a carry input. The circuit for half adder is very simple. The stimulus or the inputs of the circuit can be provided both manually or by using Terminus. For manual stimulus, use the tap switch circuit shown and used earlier. For Terminus based stimulus, connect the input with Terminus as shown in the schematic.
Components:
1. One CD4081 IC (AND Gate)
2. One CD4070 IC (XOR Gate)
3. Two 2.2KΩ Resistor, Two 10KΩ Resistor
4. Two tap switch
5. Two LED (any color)
Steps:
1. Construct the circuit as shown in the schematic (either use manual stimulation or Terminus for automated test, the steps described here is for manual stimulation)
2. Both inputs are HIGH in the beginning and both LED should be ON
3. Push tap switch of only input B to set B input LOW (i.e. input binary 0) and observe and compare the output with the truth table
4. Push tap switch of only input A to set A input LOW (i.e. input binary 0) and observe and compare the output with the truth table
5. Push both A and B input tap switch to set both of them to LOW and observe and compare the output with the truth table
Full Adder
Difference between a half adder and a full adder is full adder accepts carry while half adder does not. The circuit for a full added is two half adders with an extra OR gate. A OR gate is connected with two half adders to make it into a full adder. Schematic is given below.
Components:
1. One CD4081 IC (AND Gate)
2. One CD4071 (OR Gate)
3. One CD4070 (XOR Gate)
4. Two 2.2KΩ Resistor, Three 10KΩ Resistor
5. Three tap switch
6. Two LED (any color)
Steps:
1. Construct the circuit as shown in the schematic (either use manual stimulation or Terminus for automated test, the steps described here is for manual stimulation)
2. Both inputs are HIGH in the beginning and both LED should be ON
3. Push tap switch of only input B to set B input LOW (i.e. input binary 0), observe and compare the output with the truth table
4. Push tap switch of only input A to set A input LOW (i.e. input binary 0) and observe and compare the output with the truth table
5. Push both A and B input tap switch to set both of them to LOW and observe and compare the output with the truth table
The adders that we were working with all this time are called “ Ripple Carry Adder ”. It is called ripple carry adder because the carry is propagated across the whole chain of adders to reach the final result. To explain in more details, imagine you have a 4-bit full adder in cascade formation. To get the final result, the carry of the first stage has to propagate to the second stage before second stage can provide its calculation. After calculation on 2nd stage, the carry is propagated to the 3rd stage and then to the 4th stage. After 4th stage the complete result is presented. So the carry is propagated from 1st stage through 2nd, 3rd and 4th stage like a wave or a ripple and thus it is named “Ripple Carry Adder”.
Because the carry is propagated from one stage to later, the time requirement for the entire calculation is high. This is the reason why ripple carry adder cannot be used be used in any high speed system. In cases where high speed addition is needed, specialized adders such as Carry Skip Adder and Carry Look-ahead Adder is used.
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