Problems Set No. 5

Tanta University Faculty of Engineering Computers and Control Dept Logic Circuits & Logic Systems

Problems Set No. 5

1. Design a combinational circuit with 3 inputs and one output. The output is 1 when the binary value of the input is less than 3. The output is 0 otherwise.

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.Tthe output is 0 otherwise. Design a 3-input majority circuit.

3. Design a combinational circuit with three inputs, x, y, z, and three outputs, A, B, and C. When the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is one less than the input.

4. Develop a minimized Boolean implementation of a “ones count” circuit that works as follows. The subsystem has four binary inputs: A, B, C, D; and generates a 3-bit output: XYZ. XYZ is 000 if none of the inputs are 1, 001 if one input is 1, 010 if two are one, 011 if three inputs are 1, and 100 if all four inputs are 1. i. Draw the truth tables for X, Y, and Z. ii. Minimize the functions X, Y, Z using 4-variable K-maps. Write down the Boolean expressions for the minimized sum-of-products form of each function. iii. Repeat the minimization process, this time deriving product-of-sums form.

5. Design a combinational circuit that converts a 4-bit Gray code (see the tables below) to BCD. Decimal Gray 0 0000 1 0100 2 0101 3 0111 4 0110 5 0010 6 0011 7 0001 8 1001 9 1000 6. Design a 4-bit combinational circuit 2's complementer (the output generates the 2's complement of the input binary number).

7. Design a 4-bit combinational circuit incrementer (a circuit that adds one to a 4-bit binary number)