(a) Simplify the following Boolean expression 'A' and draw the logic diagram for the simplified expression A = ( X + YZ) + (X Y )
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- Consider the given logic equation below. Draw the logic diagram then simplify it using Boolean Algebra. Draw the logic diagram based on the simplified logic equation. X = A'BC' + A'B'C' + AB'C + AB'C' + A'B'C From the given logic diagram, trace the output using all possible input combination. Give it a conclusion upon completion..2.1 Combinational logic circuits. Tabulates a truth table for the following Boolean expression shown in Equation 1.1. f = A.B.C + A.B.C + A.B.C (1.1) 2.2 Half adder. A half adder is a circuit that adds two binary digits, A and B. It has two outputs, sum (S) and carry (C). The carry signal represents an overflow into the next digit of a multi-digit addition. Figure 1.2 depicted a logic diagram for a half adder. a. derives the Boolean expression for s and c. b. tabulates a truth table for the half adder. Ao Bo Figure 1.2: Half adder os S CDesign the following combinational logic circuit with a four-bit input and a three-bit output. The input represents two unsigned 2-bit numbers: A1 A0 and B1 B0. The output C2 C1.C0 is the result of the integer binary division A1 A0/B1 B0 rounded down to three bits. The 3-bit output has a 2-bit unsigned whole part C2 C1 and a fraction part CO. The weight of the fraction bit CO is 21. Note the quotient should be rounded down, i.e. the division 01/11 should give the outputs 00.0 (1/3 rounded down to 0) not 00.1 (1/3 rounded up to 0.5). A result of infinity should be represented as 11.1. A minimal logic implementation is not required. (Hint: start by producing a truth table of your design).
- Consider two 8-bit inputs, A = $52 and B = $C3 to the arithmetic and logic unit (ALU). Compute R =A + B. Express R in the hexadecimal form $-- : -61 Express N-Z-V-C bits in the form ----:Basic Combinational Logic Circuits 2. Write the output expression for logic circuit: A B B XIH.W: Draw a logic eircuit of the following Boolean expression before and after simplification using karnough map and Boolean expression. Y-AB+ AB A B Y 1 1
- Task 6: Simplifying Boolean functions in EWB using the logic converter Simplify the following Boolean expression in EWB using the logic converter F (A, B, C) = AB'C'+ A'B'C'+ A'BC'+ A'B'CProblem #04] Using AND and OR gates develop the logic circuit for the Boolean equation shown below. Y =AB(C + DEF) + CE(A + B +F) Problem #05] Using AND and OR gates develop the logic circuit for the Boolean equation shown below. X-A(CD+B)1. a. i. Draw the gates required to build a half adder are ii. When simplified with Boolean Algebra (x + y)(x + z) simplifies to : iii. The output of a logic gate is 1 when all its inputs are at logic 0, the gate is either :
- An X-input exclusive-OR gate and a Y-input exclusive-OR gate (where X=3, Y=4 have their outputs connected to a 2-input exclusive-NORgate. Do the following:a) Draw the logic diagram and analyze the logic expression of the output (in standard SOPform).b) List out all essential prime implicants.(m. Simplify the given expression using Boolean algebra and implement the simphifie expression using basic logic gates. Y = A.B.C+ A.B.C + A.B.C + A.B.CDraw the equivalent logic circuit diagram of the following expressions : a. XY = F b. X + Y = F XÝZ = F c. d. XY + XZ = F e. XYZ + XÝZ = F