1. A combinational circuit adds either a 1 or 2 to a 4-bit binary number A. Assume that the inputs A3, A2, A1, A0 represent the 4-bit binary number. Another input is a control signal C. The circuit has outputs assumed to be X3, X2, X1 and Xo, which represent the 4-bit number X. When C=0, X=A+1 and when C=1, X=A+2. Assume that the inputs for which X > (1111)2 will never occur. Show the design steps in detail including truth tables (10 marks), K-Maps (15 marks), logic equation minimisation (10 marks). Finally, design this circuit using only NAND gates and inverters (15 marks).

[50 marks]

2.

a. A circuit has four inputs A, B, C and D. These inputs are applied to a circuit that converts the inputs into an excess-3 code format and displays on the 7-segment indicator. Assume that only the 0 to 9 combinations (BCD) occur as inputs and the rest of the unused combinations are dont care. This means that you have a BCD to excess-3 code conversion taking place. Design a circuit for the above-mentioned process. Your design should only include NAND gates and INVERTERS.

Hint: To convert any decimal number into its excess- 3 form, add 3 to each decimal digit and then convert the sum to a BCD number For example, decimal number 3 has excess-3 form of 6, i.e., it is 0110 instead of 0011. Thus, 6 will be displayed on the 7-segment display.

b. A function is represented as below:

(,,,)= + ++

i. Use a single 8-to-1 multiplexer with active low enable and active high output to realise the above function f. Use A, C, D as selection inputs, where A is the most significant and D is the least significant. [8 marks]

ii. Use a single 4-to-1 multiplexer with active low enable and active high output and few additional gates to realise the above function f. [7 marks]