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A sequential circuit has one primary input m, and one primary output n. It has two D flip-flops with inputs D₂ and Do, and corresponding flip-flop outputs Q₂ and Q. It also has a T flip-flop with input T₁ and output Q₁. The circuit is wired in a way described by the following equations: D₂ = m'Q₂Q₁ +mQ₂'Q₁ + m²Q₂'Q₁'Qo' • T₁ = Q₁²Q₁ + mQ₁' + mQ₂'Q' + m²Q₂'Që + m²Q₂Q₁ Do = m'Q₂' + m'Q₁³Qỏ' + m²Q₁Q0 + mQ₂Q₁ Qo' n = Q₂Q₁ +mQ₁' + m'Q₂'Qo' Using the sequential circuit, perform state minimization by implication to reduce the number of states to a minimum. Which states are equivalent? In the minimized circuit, how many flip-flops are needed to implement the circuit?

A sequential circuit has one primary input m, and one primary output n. It has two D flip-flops with inputs D₂ and Do, and corresponding flip-flop outputs Q₂ and Q. It also has a T flip-flop with input T₁ and output Q₁. The circuit is wired in a way described by the following equations: D₂ = m'Q₂Q₁ +mQ₂'Q₁ + m²Q₂'Q₁'Qo' • T₁ = Q₁²Q₁ + mQ₁' + mQ₂'Q' + m²Q₂'Që + m²Q₂Q₁ Do = m'Q₂' + m'Q₁³Qỏ' + m²Q₁Q0 + mQ₂Q₁ Qo' n = Q₂Q₁ +mQ₁' + m'Q₂'Qo' Using the sequential circuit, perform state minimization by implication to reduce the number of states to a minimum. Which states are equivalent? In the minimized circuit, how many flip-flops are needed to implement the circuit?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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One example of State Minimization by Implication:
https://www.bartleby.com/questions-and-answers/suppose-you-have-one-circuit-with-three-flip-flops-t-flip-flop-with-input-t-and-output-q-d-flip-flop/eb3311d2-919a-4833-a719-950febe1ca8c

A sequential circuit has one primary input m, and one primary output n. It has two D flip-flops with inputs D₂ and Do, and corresponding flip-flop outputs Q₂ and Q. It also has a T flip-flop with input T₁ and output Q₁. The circuit is wired in a way described by the following equations: ● D₂ = m'Q₂Q₁ + mQ₂'Q₁ + m'Q₂'Q₁'Qo' T₁ = Q₁'Qo' +mQ₁' + mQ₂'Q' + m'Q₂'Qo + m'Q₂Q₁ 1 ● ● Do = m'Q₂' + m²Q₁³Qo' + m²Q₁Q0 + mQ₂Q₁ Qo' 1 n = Q₂Q₁ +mQ₁' + m'Q₂'Qo' Using the sequential circuit, perform state minimization by implication to reduce the number of states to a minimum. Which states are equivalent? In the minimized circuit, how many flip-flops are needed to implement the circuit?
Transcribed Image Text:A sequential circuit has one primary input m, and one primary output n. It has two D flip-flops with inputs D₂ and Do, and corresponding flip-flop outputs Q₂ and Q. It also has a T flip-flop with input T₁ and output Q₁. The circuit is wired in a way described by the following equations: ● D₂ = m'Q₂Q₁ + mQ₂'Q₁ + m'Q₂'Q₁'Qo' T₁ = Q₁'Qo' +mQ₁' + mQ₂'Q' + m'Q₂'Qo + m'Q₂Q₁ 1 ● ● Do = m'Q₂' + m²Q₁³Qo' + m²Q₁Q0 + mQ₂Q₁ Qo' 1 n = Q₂Q₁ +mQ₁' + m'Q₂'Qo' Using the sequential circuit, perform state minimization by implication to reduce the number of states to a minimum. Which states are equivalent? In the minimized circuit, how many flip-flops are needed to implement the circuit?
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