Consider the Boolean function F1 = X' · Z + X ' · Y · Z + X · Y ' + X · Y' · Z
(a) Implement F1, in the form as given, using 2-input ANDs, 2-input ORs and NOT gates.
How many gates did you use?
(b) Simplify F1 using Boolean algebra identities. Show all the steps & the identities used at each step.
(c) Implement the simplified form of F1 using 2-input ANDs, 2-input ORs and NOT gates.
How many gates did you use now?
Q2: 1. Proof this Boolean expression. Use Boolean Algebra (X+Y). (Z+W).(X'+Y+W) = Y.Z+X.W+Y.W 2. For this BF F(X,,Z)=((XYZ)(X +Z))(X+Y) • Design the digital circuit Derive the Boolean Function of X, Y, Z. Simplify the Function Derive the truth table before and after simplification. Derive the BF F(X,Y,Z) as Maxterms (POS) and miterms (SOP). Implement the F(X,Y,Z) after simplification using NAND gates only. Implement the F(X,Y,Z) after simplification using OR NOR gates only.
Name Use SOP, to find Boolean equation for the outputs X, Y, z Construct a logic circuit using AND, OR, and Inverter (NOT) gates which implements the Boolean equations Substitute your logic circuits with NAND gates only, simplify the circuit. 1. 2. 3. Input Outputs A B C 0 0 0 0 0 0 0 0 011 0 0 0
Simplify the following functional expression using Boolean algebra and its identities. List the identity used at each step. x(y+z)(x'+z')
L ILLLL LLLLLLL LO LLO (7) Boolean Algebra 7 marks (7a) Simplify the following logic function as a sum of products. You may use K-map. 3 marks F = Ā B D + A B D + B C D + C D + ĀB C D (76) 1 mark Implement the simplified logic function F of (7a) as a sum of products with AND and OR gates. Show your steps. You may assume complements of the literals are available....
Implement this Boolean Expression on a breadboard using NOR gates Part A: Z =XY+X 'Y' Implement this Boolean expression using only NOR gates. Apply De Morgan's law and Boolean laws for the expression to represent it only using NOR operation. Your implementation should use the minimum number of gates (4 NOR gates) required
Design a combinational circuit with three inputs, x , y, and z, and three outputs, A, B , and C . When the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is two less than the input. 1) Truth table 2) Logic circuit 3) Boolean function of A using minterms ( use Boolean algebra) 4) Boolean function of...
Computer architecture Having the next Boolean functions: F1(x,y,z)-П (1, 3, 5) . F2(x,y,z)-Σ (0, 2, 4, 5) . 1. Make one logic gate design circuit, using AND, OR and NOT logic gates (20 points). 2. Design two 4-to-1 selectors, one for each Boolean function (20 points) 3. Design one 3-to-8 decoder to solve both Boolean functions (20 points) 4. Design a 8x2 ROM to solve both Boolean functions (20 points) 5. Design a 3x5x2 PLA to solve both Boolean functions...
Simplify the Boolean function F (x, y, z) lx +y) (x'+z) and implement with two-level NOR gate circuits.
Let x,y,zϵB, where B is a Boolean algebra. Simplify (x∧y)∨(x^'∧y∧z^')∨(y∧z) As much as possible.
We are interested in designing a circuit that implements the following three Boolean functions: 3. h(x,y,z)=Σm(1,4,6) f1x,y,z)- > m(1,4,6) y-m35) (x,y, z) Σ m (2,4,6,7) 左 You are supposed to implement the circuit with a decoder constructed with NAND gates (a) [12pt] Start by drawing the block diagram of a NAND-based decoder with three inputs (x,y,z), labelling all the outputs with their corresponding Boolean functions (b) [8pt) Using a new block diagram of the NAND-based decoder, implement the circuit using...