Write in a 1 whole sheet of yellow paper. Derive the truth table, simplified Boolean function (equation), and draw the logical diagram. 1. F(A,B,C)= E (0,1,4,5,6,) 2. F(W,x,y,z) = E (1,3,4,7,10,12,13,15) 3. F(x,y,z) = n (1,3,4,5,7 ) 4. F(w,x,y,z) = T (0,1,4,5,6,8,9,11,12,14,15) 5. Implement using NAND-NAND, F= B'+CD'(A+B)+A'BC

Write in a 1 whole sheet of yellow paper. Derive the truth table, simplified Boolean function (equation), and draw the logical diagram. 1. F(A,B,C)= E (0,1,4,5,6,) 2. F(W,x,y,z) = E (1,3,4,7,10,12,13,15) 3. F(x,y,z) = n (1,3,4,5,7 ) 4. F(w,x,y,z) = T (0,1,4,5,6,8,9,11,12,14,15) 5. Implement using NAND-NAND, F= B'+CD'(A+B)+A'BC

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Derive the truth table, simplified Boolean function (equation), and draw the logical diagram. F(A,B,C)= ∑ (0,1,4,5,6,) F(w,x,y,z) = ∑ (1,3,4,7,10,12,13,15) F(x,y,z) = π (1,3,4,5,7 ) F(w,x,y,z) = π (0,1,4,5,6,8,9,11,12,14,15) Implement using NAND-NAND, F= B'+CD'(A+B)+A'BC
Derive the truth table, simplified Boolean function (equation), and draw the logical diagram. F(A,B,C)= ∑ (0,1,4,5,6,) F(w,x,y,z) = ∑ (1,3,4,7,10,12,13,15) F(x,y,z) = π (1,3,4,5,7 )
Show using a truth table if the following statements are equivalent.a. ~(p ∨ q) and ~p ∧ ~qb. p → q and ~p ∨ qc. p ↔ q and [(p → q) ∧ (q → p)]d. p → (q ∨ r) and (p → q) ∨ (p → r)e. [p ↔ (q ∨ r)] ∨ q and (p → q) ∨ (p ↔ r)
2. Simplify the following Boolean expressions, using three variable K-maps: (a) F(x,y,z) = xy+x′y′z′+x′yz′ (b) F(x,y,z) = x′y′+yz+x′yz′ (c) F(x,y,z) = x′y+yz′+y′z′
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Use a truth table to demonstrate that these two statements are logically equivalent:((p ∧ ¬q) ∨ (p ∧ q)) ∧ q and (p ∧ q).
Consider a logic function with inputs A, B, and C defi ned as follows: ■ If A or C is true, then output D is true, whatever the value of B. ■ If A or B is true, then output E is true, whatever the value of C. ■ Output F is true if exactly one of the inputs is true, although we don’t care about the value of F, whenever D and E are both true. Show the full truth table for this function and the truth table using don’t cares. How many product terms are required in a PLA for each of these?
Is my truth table correct for the following conditions? If W is greater than X , then A is 1, B and C are 0. If W equals X, then B is 1, A and C are 0. If W is less than X, C is 1, A and B are 0.
4. Simplify the following Boolean expressions, using four-variable K-maps: (a) A′B′C′D′+AC′D′+B′CD′+A′BCD+BC′D (b) w′z+xz+x′y+wx′z
Show that the following two formulas are NOT logically equivalent by giving a model in which one is true and the other is false: ∃x ( R(x) → S(x) ) and ¬ ∀x ( R(x) ∧ S(x) )
not handwritten Consider CNF below. (D(y) ∨ E(y)) ∧ (D(y) ∨ ¬E(Miles)) ∧ ¬D(Carl) Variable y is universally quantified. Show that the expression always evaluates to false.
Express the following in canonical forms , simplify using KMAP and make a truth table of the simplified expression: F(A, B, C, D) = ∑ (0, 1,2,5,8,9, 10)