Question

Design a circuit that has four inputs and three outputs. Output one indicates whether the two’s complement signed 4 bit input is larger than 5, output two indicates if the signed 4 bit input is smaller than -5, and output three indicates that the signed 4 bit input is equal to zero. Provide the initial equations that describe your circuit and minimize your output equations using k-maps. Draw your circuits from the minimized equations using AND, OR, and NOT gates.

Answer 1

To design a circuit with four inputs and three outputs, we can analyze each output condition separately and combine them using AND, OR, and NOT gates. Output one checks if the two's complement signed 4-bit input is larger than 5, output two checks if the input is smaller than -5, and output three checks if the input is equal to zero.

Step-by-step explanation:

To design a circuit with four inputs and three outputs, we can start by analyzing each output condition separately and then combine them into a single circuit. For output one, we need to check if the two's complement signed 4-bit input is larger than 5. We can compare the most significant bit (MSB) of the input to 0. If the MSB is 0, it means the number is positive, and we can check if the input is greater than 5. If the MSB is 1, it means the number is negative, and we can conclude that it is larger than 5. We can use AND, OR, and NOT gates to implement this logic.

For output two, we need to check if the signed 4-bit input is smaller than -5. We can compare the MSB of the input to 1. If the MSB is 0, it means the number is positive and not smaller than -5. If the MSB is 1, we can compare the input to -5. Again, we can use AND, OR, and NOT gates to implement this logic.

For output three, we need to check if the signed 4-bit input is equal to zero. We can check if all the bits of the input are 0. We can use OR gates to implement this logic.