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X Y Z a b cin Cout Cout Find the minimal SOP and POS representation of...
1. (8 points) Obtain a minimal SOP form for the boolean function f(x,y,z,w) implemented by logic...
1. (8 points) Obtain a minimal SOP form for the boolean function f(x,y,z,w) implemented by logic network below. Compare the gate count and number of gate inputs in your minimal SOP expression with those for the network below. f(x,y,z,w)
Q31 For the figure shown below W is an input, (X, Y and Z) are connected...
Q31 For the figure shown below W is an input, (X, Y and Z) are connected to (S2, S and So), find the Boolean function F (W, X, Y, Z) in SOP and implement it use: 1. Multiplexer: One-piece (4 to 1) and external gates (W, X are selectors). 2. Decoder: Five (2 to 4) with AND gate. 0 1 8 to 1 MUX Do D, F OP D, S S S 35 Marks] X Y Z
Q31 For the...
3.41 Given the circuit below, find the minimum SOP expression for f(W,X,Y,Z). 4-10-16 Decoder 1 NO...
3.41 Given the circuit below, find the minimum SOP expression for f(W,X,Y,Z). 4-10-16 Decoder 1 NO ZA ܩܘܩܩܩܩܩܩܩܩܩܩܩܩܩܩ
a full-adder circuit is used to add 2 bits A and B and the carry (Cin)...
a full-adder circuit is used to add 2 bits A and B and the carry (Cin) that resulted from the addition of the previous 2 bits. It then produces a SUM S and a carry out (Cout) that would be added to the more significant bits. Generate a truth table that has inputs A, B and Cin and the 2 outputs S and Cout. Find the logical function from the truth table and simplify it, if possible. Implement the function...
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...
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...
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
Class 24 1. Given the shorthand POS expression F(a,b,c,d) П M (0,6,7,8) (b + c + d)(a + D+ ē): a....
Class 24 1. Given the shorthand POS expression F(a,b,c,d) П M (0,6,7,8) (b + c + d)(a + D+ ē): a. (25 points) Implement F using one 4-to-16 decoder and one OR gate of any size. b. (25 points) Implement F using four 2-40-4 decoders and one OR gate of any size. c. (25 points) Implement F using just two 8-to-3 encoders, NOT gates, and one AND gate of any size. Hint: given NOT gates and an AND gate to...
Implement the function F (x,y,z)= (not x)(not z)+ xy using a. One 4-to-1 multiplexer and any...
Implement the function F (x,y,z)= (not x)(not z)+ xy using a. One 4-to-1 multiplexer and any additional inverters. Show your truth-table and justify your choice of select inputs. b. One 2-to-1 multiplexer and the minimal number of gates. Show the truth table used to derive your circuit.
We are interested in designing a circuit that implements the following three Boolean functions: 3. h(x,y,z)=Σm(1,4,6)...
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...
1. Use K-maps to reduce each of the following to a minimized SOP form: (a) A...
1. Use K-maps to reduce each of the following to a minimized SOP form: (a) A + BC + CD (b) ABCD + ABCD + ABCD + ABCD (c) ABCD + CD) + ABCD + CD) + ABCD (d) (AB + ABXCD + CD) (e) AB + AB + CD + CD 2. Use K-maps to find the minimum SOP expression for the logic function shown in the table to the right. Implement the circuit using NAND gates only. Inputs...
1. (8 points) Obtain a minimal SOP form for the boolean function f(x,y,z,w) implemented by logic network below. Compare the gate count and number of gate inputs in your minimal SOP expression with those for the network below. f(x,y,z,w)
Q31 For the figure shown below W is an input, (X, Y and Z) are connected to (S2, S and So), find the Boolean function F (W, X, Y, Z) in SOP and implement it use: 1. Multiplexer: One-piece (4 to 1) and external gates (W, X are selectors). 2. Decoder: Five (2 to 4) with AND gate. 0 1 8 to 1 MUX Do D, F OP D, S S S 35 Marks] X Y Z
Q31 For the...
3.41 Given the circuit below, find the minimum SOP expression for f(W,X,Y,Z). 4-10-16 Decoder 1 NO ZA ܩܘܩܩܩܩܩܩܩܩܩܩܩܩܩܩ
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
Class 24 1. Given the shorthand POS expression F(a,b,c,d) П M (0,6,7,8) (b + c + d)(a + D+ ē): a. (25 points) Implement F using one 4-to-16 decoder and one OR gate of any size. b. (25 points) Implement F using four 2-40-4 decoders and one OR gate of any size. c. (25 points) Implement F using just two 8-to-3 encoders, NOT gates, and one AND gate of any size. Hint: given NOT gates and an AND gate to...
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...
1. Use K-maps to reduce each of the following to a minimized SOP form: (a) A + BC + CD (b) ABCD + ABCD + ABCD + ABCD (c) ABCD + CD) + ABCD + CD) + ABCD (d) (AB + ABXCD + CD) (e) AB + AB + CD + CD 2. Use K-maps to find the minimum SOP expression for the logic function shown in the table to the right. Implement the circuit using NAND gates only. Inputs...
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