Question

For the following design problem, make a truth table that describes the problem, then and draw a logic diagram of the circuit (you can draw the diagram by hand). The circuit should use a 4:16 Decoder with negated outputs (low) and any other logic gates: NOT, AND, OR, NAND, NOR, XOR. The logic gates in this design may have multibit inputs.

Design a logic circuit that will output HIGH when the input is an odd number less than 8, and an even number greater than or equal to 8, and all inputs are smaller than 16. The input should be a 4-bit binary number. Design the circuit using a 4:16 decoder and other gates.

Answer 1

A logic circuit utilizing a 4:16 Decoder with negated outputs is designed to output HIGH for an odd number less than 8 and an even number greater than or equal to 8. The desired output values are represented in a truth table with binary inputs less than 16, and the circuit is described sequentially using NOT and OR gates to achieve the specified conditions.

Step-by-step explanation:

The student's design problem involves creating a logic circuit that outputs HIGH for an odd number less than 8 and an even number greater than or equal to 8, with the condition that all inputs are smaller than 16. For this to be accomplished, we need to build a truth table for a 4-bit input and determine when the output should be HIGH based on the conditions provided.

Firstly, let's construct the truth table considering a 4-bit binary input (W, X, Y, Z) where Z is the least significant bit:

• Odd and less than 8: 0001, 0011, 0101, 0111.
• Even and greater than or equal to 8: 1000, 1010, 1100, 1110.

Now, we design the circuit using a 4:16 Decoder with negated outputs and combine the relevant outputs using OR gates to produce the desired HIGH output when the input conditions are met. The outputs from the decoder corresponding to the binary values 1 (0001), 3 (0011), 5 (0101), 7 (0111), 8 (1000), 10 (1010), 12 (1100), and 14 (1110) are ORed together. Since the decoder outputs are negated, we would need to invert these outputs before the OR gate.

It is important to note that I cannot draw an actual diagram here, but I can describe it in detail:

1. 
   
3. Create inverters (NOT gates) to negate the outputs from the decoder corresponding to the binary values mentioned.
4. 
   
6. Feed these negated outputs into an OR gate to create the final output.

This circuit will thus output HIGH for an odd number less than 8 and an even number greater than or equal to 8, according to the initial design requirement.