2. Design a combinational circuit that accepts a three bit binary number as input, and produces the two's complement of that number as output. Draw the logic diagram. (1 point for design, 1 point for diagram) 3. Design a circuit that detects errors in 8421 BCD digits. If the input is a valid digit the circuit outputs a 1. If the input is not a valid digit the circuit outputs a 0. (1 point for design) 4. Design a circuit that accepts a three bit input, which we will view as a string, and as output delivers the string after a circular shift to the right. If you are not familiar with this shift, it's fairly simple. Each bit in the string moves one position to the right, and the bit that would normally fall off of the right end is brought around to the left side of the string. Examples: if input combination is 001, output is 100; if input is 011, output is 101; if input is 101, output is 110; etc. Draw the logic diagram. (1 point for design, 1 point for diagram) 5. Design a combinational circuit that accepts a three- bit binary number as input. The circuit outputs a if that number is a multiple of four, otherwise it outputs a 0. (1 point for design) 1. Reduce the following Sum of Minterm expressions to minimal Sum of Product form using K-Maps (1 point each): a. Flx,y) = {m(0, 1, 3) b. F(x,y,z) = x'yz + xy'z + xyz + xyz + xyz C. F[w.x.y,z) = w'xy'z + w'x'y'z + w'xyz + w'xyz' + wxy'z' + wx'yz + wxy'z + wxyz d. Flv,w.X.y.z) = m(0, 2, 5, 8, 10, 12, 13, 16, 18, 21, 24, 26, 30, 31) 2. Design a combinational circuit that accepts a three bit binary number as input, and produces the two's complement of that number as output. Draw the logic diagram. (1 point for design, 1 point for diagram) 3. Design a circuit that detects errors in 8421 BCD digits. If the input is a valid digit the circuit outputs a 1. If the input is not a valid digit the circuit outputs a 0. (1 point for design) 4. Design a circuit that accepts a three bit input, which we will view as a string, and as output delivers the string after a circular shift to the right. If you are not familiar with this shift, it's fairly simple. Each bit in the string moves one position to the right, and the bit that would normally fall off of the right end is brought around to the left side of the string. Examples: if input combination is 001, output is 100; if input is 011. output is 101; if input is 101, output is 110; etc. Draw the logic diagram. (1 point for design, 1 point for diagram) 5. Design a combinational circuit that accepts a three- bit binary number as input. The circuit outputs a if that number is a multiple of four otherwise it outputs a 0. (1 point for design)
