Digital Logic & State Machine Design

1) Consider the following combinational circuit with 4 inputs and 3 outputs. Answer i & ii (in image)

2) Consider the following combinational circuit with four inputs and three outputs. Note that there are 8 inputs, therefore a truth table is impractical. Obtain an OPERATION TABLE that groups input combinations into a few categories. What is its purpose, must include meaning of each output (R, Y, and Z).

3) Consider the combinational circuits with 4 inputs and two outputs, and its implementation with 4 components: a) Obtain the truth table. b) Obtain the minterm list from the truth table

1) Consider the following circuit with four inputs and three outputs 2(a, b, c, d) z1(a, b, c, d)z z0(a, b, c, d) Operation Table a b Operation msb 101 111 Z=K+1 K is a 2-bit 2's Complement Binary number Z is a 3-bit 2's Complement Binary number Z=K-1 (i) Obtain the truth table of the combinational circuit based on the operation table. In a single sentence can you describe what this circuit does, i.e. its purpose? In order for K to have three bits so that it has the same bits as Z, assume that K has an invisible third (leftmost) bit whose value is obtained via a sign extension on K. Then perform the neces- sary operation on K. Name this invisible leftmost bit as "e and show it on your truth table. (i) Then, obtain the minterm lists of the outputs from the truth table. 1) Consider the following circuit with four inputs and three outputs 2(a, b, c, d) z1(a, b, c, d)z z0(a, b, c, d) Operation Table a b Operation msb 101 111 Z=K+1 K is a 2-bit 2's Complement Binary number Z is a 3-bit 2's Complement Binary number Z=K-1 (i) Obtain the truth table of the combinational circuit based on the operation table. In a single sentence can you describe what this circuit does, i.e. its purpose? In order for K to have three bits so that it has the same bits as Z, assume that K has an invisible third (leftmost) bit whose value is obtained via a sign extension on K. Then perform the neces- sary operation on K. Name this invisible leftmost bit as "e and show it on your truth table. (i) Then, obtain the minterm lists of the outputs from the truth table