[1] Consider a Boolean Algebra Show that (a) xy+xz+yz=x.y + x'.z (b) (a+b)'(a'+by=0 [2] Algebraically simply the following expressions: (a) F=abc + abc + ab'c+abe'+ab'e (b) F=y(wz wz) + xy [3] Simplify the following Boolean expressions to a minimum number of literals: (a) xy + xy (b) (x+y)(x + 9) (c) xyz + 2y + xyz (d) (A+B) (A + B) [4] Reduce the following Boolean expressions to the indicated number of literals: (a) XC + ABC + AC (b) (19+2)+z+ xy +wx (c) AB(D+CD) + B(A + ACD) (d) (+C)(+C)(A + B + CD) [5] Find the complement of the following expressions: (a) xỹ + Ry (b)(a + c)(a + b)(a + b + c) (c) z+ 2(0w + xy) (d) (w +92)(x + Wz) [6] Given F= ab + b(ad + ac) implement it with AND, OR and inverter gates. [7] Implement the Boolean function F = xy +9z (a) With AND, OR, and inverter gates (b) With OR and inverter gates (c) With AND and inverter gates (d) With NAND and inverter gates (e) With NOR and inverter gates to three literals. to three literals. to one literals. to four literals.

[1] Consider a Boolean Algebra Show that (a) xy+xz+yz=x.y + x'.z (b) (a+b)'(a'+by=0 [2] Algebraically simply the following expressions: (a) F=abc + abc + ab'c+abe'+ab'e (b) F=y(wz wz) + xy [3] Simplify the following Boolean expressions to a minimum number of literals: (a) xy + xy (b) (x+y)(x + 9) (c) xyz + 2y + xyz (d) (A+B) (A + B) [4] Reduce the following Boolean expressions to the indicated number of literals: (a) XC + ABC + AC (b) (19+2)+z+ xy +wx (c) AB(D+CD) + B(A + ACD) (d) (+C)(+C)(A + B + CD) [5] Find the complement of the following expressions: (a) xỹ + Ry (b)(a + c)(a + b)(a + b + c) (c) z+ 2(0w + xy) (d) (w +92)(x + Wz) [6] Given F= ab + b(ad + ac) implement it with AND, OR and inverter gates. [7] Implement the Boolean function F = xy +9z (a) With AND, OR, and inverter gates (b) With OR and inverter gates (c) With AND and inverter gates (d) With NAND and inverter gates (e) With NOR and inverter gates to three literals. to three literals. to one literals. to four literals.

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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Source:https://www.mog.dog/files/SP2019/Sipser_Introduction.to.the.Theory.of.Computation.3E.pdf
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