Question

A given circuit has four inputs.

Two of the inputs are considered the fractional portion of a binary number while the other two inputs are considered the integral portion of the binary number.
The outputs of this circuit should represent a 2-bit binary number associated with the 4-bit input but with rounding up and down.
In other words, if the input is greater or equal to 0.5, the output should represent the input rounded up. Otherwise, it output should represent the input rounded down to the nearest integer.
Note: For this exercise you may assume that the input will never be larger than can be represented by the output, in other words, it will not overflow.
You may treat any overflow input conditions as don’t cares.
Provide a truth table, a reduced Boolean equation and circuit diagram for your solution using AND, OR, and NOT gates.

Answer 1

The given circuit has four inputs and is designed to round up or down a 4-bit binary number based on specific conditions. The truth table, Boolean equation, and circuit diagram are provided.

Step-by-step explanation:

The given circuit has four inputs, with two inputs representing the fractional portion of a binary number and the other two inputs representing the integral portion of the binary number.

The outputs of this circuit should represent a 2-bit binary number associated with the 4-bit input but with rounding up and down. If the input is greater or equal to 0.5, the output should represent the input rounded up. Otherwise, the output should represent the input rounded down to the nearest integer.

Here is the truth table, Boolean equation, and circuit diagram for this solution:

Truth table:

InputOutput0000010010011110

Boolean equation: output = ((A nor B) and C) or (A and (B nor C))

Circuit diagram: