Implement f (a, b, c, d) = Σ m(3, 4, 5, 6, 7, 11, 15) as a two-level gate circuit, using a minimum number of gates. (a) Use AND gates and NAND gates. (b) Use OR gates and NAND gates. (c) Use NAND gates only.

• What is the output function F of the following circuit in the standard sum of product Which gate can be used to replace the circuit (it has 3 NAND and 1 AND) by one of the following gates. (AND, OR, NAND, NOR, XOR, XNOR) y ×

Alternatively, we can take a mathematical approach and reduce the gate count to 4 by starting with F2 = (A + B) (A + B). (Hint: distribute the content in the second parentheses and then do De Morgan's Law several times.) Convince yourself that F1 is equivalent to F2 by the distributive property. Draw the above Boolean expression F2 by using only four 2-input NAND gates based on the above method.

Apply Boolean algebra simplification rules to Simplify the Boolean expression F = A'B + BC' + A'BC. Draw the circuit diagram of the simplified term using minimum number of gates.

The truth table for an "OR' gatë combing A and B to give C is (C) C 1 (A) A. В (B) A 1 1 1 1 1 1 1 1 1 1 1 (D) A. 1

Excersize 1: Sketch a schematic of the circuit described by the following VHDL code. Simplify the schematic so that it shows a minimum number of gates. library IEEE; use IEEE.STD_LOGIC_1164.all; entity exercisel is port (a, b, c: in Y, 2: STD LOGIC; out STD LOGIC); end; architecture synth of exercisel is begin y <= (a and b and c) or (a and not b and c); z <= (a and b) or (not a and not b); end; (a and b and not c) or

One way to think of logic gate types is to consider what input states guarantee a certain output state. For example, we could describe the function of an AND gate as “Any low input guarantees a low output.” Identify what type of gate is represented by the following phrase: “Any low input guarantees a high output.”

Build the logic circuit, using AND and OR gates and INVERTERS. Z = [A + B + C'DE ']' + B'CD ' Also, Evaluate the output of the circuit for A = B = D =0 and C= E = 1 (Hint: Use Z equation and substitute the variables with the numerical inputs given and do your analysis)