Assignment

1. Design a combinational circuit with four inputs, x,y,w, and z, and four outputs: A, B, C, and D. When the binary input value in decimal is 1,3,5,7,9,11,13 or 15, the binary output value is one less than the input value, otherwise it is one greater than the input. You can only use full adders and inverter gates to build your circuit.

2. A majority circuit is a combinational circuit whose output is equal to 1 if the input variables have more 1's than 0's. The output is 0 otherwise. Design a 5-input majority circuit.

3. Design an 8-bit combinational circuit that produces the magnitude of a binary number presented at the input. The number at the input is in 2's complement. Only half adders and four gates of your choice are available.

4. Consider the following circuit:

The input combinations (x,y,w,z) = (0,1,1,1), (1,1,0,1) never occur. Simplify the circuit such that the simplified and the old circuit produce the same output values for those input combinations that may occur.

5. Draw gate-level implementations of a 4-bit ripple carry adder and a 4-bit carry-look-ahead adder.

Indicate the critical (longest) path in each adder. State number of gate delays for each path.

What input patterns activate these paths?