Task 1: Adders Half Adder The basic unit of an adding circuit is called the Half Adder (HA). The circuit has two binary inputs (A & B) and only two outputs (Sum and Carry-Out). The Block diagram and truth table is shown in Figure 6. A Sum A B 00 Sum Carry 0 HA 0 1 1 0 B Carry D 10 1 0 1 1 0 1 Figure 1: Half Adder Block diagram and Truth Table Write down the Boolean expression from the HA truth table of the Sum output and the Boolean expression from the HA truth table of the Carry output. Construct a half adder in Multisim, using TTL NAND gates. Use some switches and indicators to demonstrate that it works. Task 2: Full Adders The Half-Adder, as described above, is limited in the fact that it cannot be cascaded due to it not having a Carry-In input (the Carry-Out from the previous unit). The Full-Adder (consisting of two Half- Adders), however, addresses this situation, and is the basis for the addition and subtraction units within a computer. A A Sum A Sum Sum HA HA BB Carry B Carry Cin D Cout Figure 2: Full-Adder using two Half-Adder blocks Note that subtraction can be viewed as the addition of a negative number, and therefore can be performed by a Full-Adder. Figure 7 shows how a Full-Adder can be formed from two Half-Adders and an 'OR' gate and Figure 8 shows the block diagram for a Full-Adder. A Sum B FA Cin Cout Figure 8: Full-Adder Block diagram Complete the truth table for a Full Adder. Construct a full adder, using the previously constructed half adder as hierarchical block. Use some switches and indicators to demonstrate that it works and make screenshots to show this. Task 3: 4-bit Binary Adder Full adders can be combined to form 2 or 4 bit adders. Construct a 4-bit binary adder using the full adder you constructed before as hierarchical block. Connect the binary adder to the switch inputs and logical probes as shown below. Add a binary number A on switches A0-A3 (termed the augend), to a binary number B with switch inputs B0 to B3 (termed the addend), and check that the correct output appears. A3 and B3 are the most significant binary digits. Convert the last and the second last digit of your student number to binary and add them together. Make screenshots of the simulated circuit showing the result.