1. Draw out the truth-table for the XOR function. Make this using only NAND gates. Define and use DeMorgan's theorem both in Boolean and diagrammatic terms in the solution. Why is the EXOR function considered useful in binary addition circuits'
As per Mano (2000, p.47), "The generalised form of DeMorgan's theorem states that the complement of a function is obtained by interchanging AND and OR operators and complementing each literal." This can be expressed algebraically as follows:
A binary input of 0100 would light four LEDs in a row whilst a binary input of 0101 would light five LEDs in a row. Derive the truth-table for a 4 bit input/ 16 bit output decoder which would be used to power this linear display.
Solution: Let x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 and x15 represent the linear array of LEDs. Let A, B, C and D represent the binary input terminals. The truth-table for the linear display is shown in Figure 2.2.