Problem: Derive the logic expressions for a circuit that compares two unsigned numbers: X = x2x₁x0 and Y = y2y1yo and generates three outputs: XGY, XEY, and XLY. One of these outputs is set to 1 to indicate that X is greater than, equal to, or less than Y, respectively.
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- Design a 4-bit arithmetic circuit, with two selection variables S1 and S0, that generates the arithmetic operations in the following table. Draw the logic diagram for a single bit stage. Note that B’ represents “Not B”. Draw the logic diagram for a single bit stagA combinational logic circuit that compares between two 2-bit numbers A (A1 A0) and B(B1 B0) is designed. Output F is high when ? > ? and low when ? < ?. 1) Are there any undefined outputs? If there are any undefined outputs what are the inputs?Determine the simplified Sum of Product expression of Q1 and Q2 from the table using a K-Map, then draw the simplified logic diagram. SHOW KMAP WITH THE FINAL EXPRESSION & LOGIC DIAGRAM
- (1) Find out the logic expression of output Q for the circuit on the left. And prove this is equivalent to the D latch circuit on the right. (2) Explain which is better and why?Using the analysis technique where you first extract the truth table and then use it to derive the output’s logic expression, analyze the circuit. Record your results below. I added the circuit as an image Conclusion In your own words, describe the process used to analyze a logic circuit where you first extract a truth table and then derive the logic expression. 2.Again, in your own words, describe the process used to analyze a logic circuit where you first extract the logic expression and then derive the truth table.Examine the circuit given below. Write the expression for outputs Q1, Q2, and Q. Clearly indicate which logic gate Q output is using Boolean Algebra and write the name of this logic gate.
- 1. Given the Boolean expression (b + d)(a’+ b’ + c),a. Convert the expression to the other standard form. What do you call this standard form?b. Derive its canonical form. What do you call this canonical form?c. Derive the other canonical form. What do you call this canonical form?d. Provide the truth table of the expressione. Draw the logic circuit diagrams of the 2 standard formsA circuit which takes a binary-coded decimal (BCD) number as input s to be designed such that the single output Q is true if the input is a prime number (remerber that 0 and 1 count as prime numbers). (a)Draw a truth table that specifies the above circuit (b)Using the truth table you have constructed and the Karnaugh map method find the minimised Boolean expression for the output Q. (c)Implement the digital circuit using the minimum number of 2-input logic AND, OR gates and inverters (NOT.1-Using the Karnaugh Method, design and draw the circuit of the logic circuit that gives the result of the multiplication of the two-bit numbers "AB" and "CD" according to minterms (SOP). Do not make any further simplifications before or after the Karnaugh Method. In tables and Karnaugh, ensure that the least significant bit is on the far right and the entries are sorted alphabetically. Make sure that the circuit you have drawn is understandable, the function you have written and the truth table are readable.
- Using a 4-bit signed input P=P3P2P1P0 and a control input Z, use a 4-bit adder and any logicgates to design a digital circuit that does the following: ● Outputs P + 3, if the input Z = 0● Outputs P − 3, if the input Z = 1 You can ignore cases where an overflow* might occur after performing the addition or subtraction operation, as long as the circuit performs the signed binary arithmetic correctly. *In computers, typically there is additional circuitry for an overflow flag that gets triggered when the result of an arithmetic operation “does not fit” the number of bits allocated for the output. Please ensure that your components, such as your 4-bit adder are shown clearly with the complete labels of their input and output pins and signals. The sample diagram below shows examples of these labels.is it possible to connect the outputs of a comparator to a logic gate (connected to an led)? The led connected to the logic gate lights up if the inputs of the comparator both satisfy a condition, for example, the voltage of both inputs are less than the reference voltages.DIGITAL LOGICGiven the two binary numbers X = 1000100 and Y = 100101 , perform the subtraction X - Y by using 1's complement and 2's complement.