Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 34.3, Problem 1E
Program Plan Intro
To verify the given circuit in the Figure
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Find a Hamiltonian circuit inCay({(a, 0), (b, 0), (e, 1)}:Q4 ⊕ Z2).
6. For the truth table below, write its Boolean expression in canonical SOP form,
then draw the circuit. Using the Boolean algebra rules, simplify the circuit (do NOT
use a K-map) to a simpler SOP form and draw that SOP circuit.
X
1
1
1
1
1
1
1
1
1
1
1
1
1
1
The NAND logic gate is universal, meaning that using gate alone,
we can implement any of the other logic gates. Find a way to define
NOT, AND, and OR, using only NAND gates and the input variables
I and y.
(a) NOT(2) =
(b) AND(x, y) =
(c) OR(x, y) =
Chapter 34 Solutions
Introduction to Algorithms
Ch. 34.1 - Prob. 1ECh. 34.1 - Prob. 2ECh. 34.1 - Prob. 3ECh. 34.1 - Prob. 4ECh. 34.1 - Prob. 5ECh. 34.1 - Prob. 6ECh. 34.2 - Prob. 1ECh. 34.2 - Prob. 2ECh. 34.2 - Prob. 3ECh. 34.2 - Prob. 4E
Ch. 34.2 - Prob. 5ECh. 34.2 - Prob. 6ECh. 34.2 - Prob. 7ECh. 34.2 - Prob. 8ECh. 34.2 - Prob. 9ECh. 34.2 - Prob. 10ECh. 34.2 - Prob. 11ECh. 34.3 - Prob. 1ECh. 34.3 - Prob. 2ECh. 34.3 - Prob. 3ECh. 34.3 - Prob. 4ECh. 34.3 - Prob. 5ECh. 34.3 - Prob. 6ECh. 34.3 - Prob. 7ECh. 34.3 - Prob. 8ECh. 34.4 - Prob. 1ECh. 34.4 - Prob. 2ECh. 34.4 - Prob. 3ECh. 34.4 - Prob. 4ECh. 34.4 - Prob. 5ECh. 34.4 - Prob. 6ECh. 34.4 - Prob. 7ECh. 34.5 - Prob. 1ECh. 34.5 - Prob. 2ECh. 34.5 - Prob. 3ECh. 34.5 - Prob. 4ECh. 34.5 - Prob. 5ECh. 34.5 - Prob. 6ECh. 34.5 - Prob. 7ECh. 34.5 - Prob. 8ECh. 34 - Prob. 1PCh. 34 - Prob. 2PCh. 34 - Prob. 3PCh. 34 - Prob. 4P
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- Develop the truth table of the logic circuit. Simplify the equation by using Karnaugh Maps. Implement the simplified equation (draw the circuit diagram) by using gates.arrow_forwardGate Universality We know that the NAND gate is universal, so all other gates can be built using just NAND gates. We also mentioned that the NOR gate is universal, and can serve the same purpose. In this question we will look at NOR gates. Draw the AND operation as a circuit using a minimal number of NOR gates. Check your design in (a) by showing the full truth table for it. Draw the OR operation as a circuit using a minimal number of NOR gates. Check your design in (c) by showing the full truth table for it. Draw the NOT operation as a circuit using a minimal number of NOR gates. Check your design in (e) by showing the full truth table for it.arrow_forwardb- For the following truth table, define its combinational circuit, and realize it using its K-map. АВС Y Z 0 0 0. 1 0. 1 0 1 0 1 1 0 1 1 0. 0 1 101 1 1 1010 1 1 1 1 1arrow_forward
- Show that these two circuits are equivalent by two methodsarrow_forwardSimplify the Boolean function with K-Map method and implement the logic circuit using minimum number of NAND gates. F(A,B,C,D) = Σ m (0,1,3,4,7,8,11,12) + Σ d (0,5,14,15)arrow_forwardFind a Hamiltonian circuit in Cay({(a, 0), (b, 0), (e, 1)}:Q4 ⊕ Zm) where m is even.arrow_forward
- Implement the following Boolean function by using NAND gates only.F(A,B,C,D) = ∑ (1,3,4,8,10,11,13,14)arrow_forwardShow that the output carry in a full-adder circuit can be expressed in the AND–OR–INVERT form C i + 1 = G i + P i C i = ( G i ′ P i ′ + G i ′ C i ′ ) ′ (IC type 74182 is a lookahead carry generator circuit that generates the carries with AND–OR–INVERT gates (see Section 3.8 ). The circuit assumes that the input terminals have the complements of the G’s, the P’s, and of C 1 . Derive the Boolean functions for the lookahead carries C 2 , C 3 , and C 4 in this IC.arrow_forwardImplement the circuit defined by equation F(a,b,c,d) = E (0,5,6,7,11) using: 4-to-1 multiplexers and logic gates. 2-to-4 decoders with non-inverted outputs and logic gates. i. ii.arrow_forward
- Simplify the following expression and implement it using NOR gate. F(A,B,C,D)=Em(1,2,4,11,13,14,15)+Ed(0,5,7,8,10)arrow_forwardFind a Hamiltonian circuit inCay({(a, 0), (b, 0), (e, 1)}:Q4 ⊕ Zm) for all odd m ≥ 3.arrow_forwardGiven the Boolean function f (A,B,C,D)-Em(1, 3, 9, 10) +Ed(0,2,8,13). a. Simplify the function using k-Map? b. Implement the function using standard gates? c. Implement the function using only NAND gates? d. Implement the function using only NOR gates?arrow_forward
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