1-Convert the Boolean expression to SOP form: AB +B(CD+EF)<\/p>\n\n\n\n
2-Convert the Boolean expression to standard SOP form: AB +\u0100BD+\u0100CD 3-Express F = % \u1ef9 + x Z in a standard (POs) form, then write F in conical (E T) forms. Draw the logic circuit of F.<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n Let’s break each part down carefully and provide a thorough explanation.<\/p>\n\n\n\n Given expression: Expanding using distribution: Given expression: Each term should have all variables (A, B, C, and D) explicitly present.<\/p>\n\n\n\n Now, collecting all minterms: Given function: To convert to POS, use De Morgan\u2019s theorem<\/strong> and distributive laws:<\/p>\n\n\n\n Thus, the POS form<\/strong> is: Identify the minterms by writing a truth table.<\/p>\n\n\n\n Minterms where F = 1<\/strong>: ( m_4, m_5, m_6, m_7 )<\/p>\n\n\n\n [ The logic circuit consists of:<\/p>\n\n\n\n The circuit:<\/p>\n\n\n\n 1-Convert the Boolean expression to SOP form: AB +B(CD+EF) 2-Convert the Boolean expression to standard SOP form: AB +\u0100BD+\u0100CD 3-Express F = % \u1ef9 + x Z in a standard (POs) form, then write F in conical (E T) forms. Draw the logic circuit of F. The correct answer and explanation is : Let’s break […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-199727","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199727","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=199727"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199727\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199727"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199727"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199727"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n1. Convert the Boolean expression to Sum of Products (SOP) Form:<\/strong><\/h3>\n\n\n\n
[
AB + B(CD + EF)
]<\/p>\n\n\n\n
[
AB + BCD + BEF
]
This is already in SOP form because it is a sum of product terms.<\/p>\n\n\n\n
\n\n\n\n2. Convert the Boolean expression to Standard SOP Form:<\/strong><\/h3>\n\n\n\n
[
AB + \\bar{A}BD + \\bar{A}CD
]<\/p>\n\n\n\n\n
[
AB = ABCD + ABC\\bar{D} + AB\\bar{C}D + AB\\bar{C}\\bar{D}
]<\/li>\n\n\n\n
[
\\bar{A}BD = \\bar{A}BCD + \\bar{A}B\\bar{C}D
]<\/li>\n\n\n\n
[
\\bar{A}CD = \\bar{A}BCD + \\bar{A}\\bar{B}CD
]<\/li>\n<\/ul>\n\n\n\n
[
ABC\\bar{D} + AB\\bar{C}D + AB\\bar{C}\\bar{D} + \\bar{A}BCD + \\bar{A}B\\bar{C}D + \\bar{A}\\bar{B}CD
]
This is the standard SOP form.<\/p>\n\n\n\n
\n\n\n\n3. Express ( F = x \\bar{y} + xz ) in Standard POS and Canonical Form<\/strong><\/h3>\n\n\n\n
[
F = x\\bar{y} + xz
]<\/p>\n\n\n\nConvert to POS (Product of Sums) form<\/strong><\/h4>\n\n\n\n
\n
[
F’ = (x\\bar{y} + xz)’ = (x\\bar{y})'(xz)’
]<\/li>\n\n\n\n
[
(x + y)(\\bar{x} + \\bar{z})
]<\/li>\n\n\n\n
[
F = (x + y)(\\bar{x} + \\bar{z})
]<\/li>\n<\/ol>\n\n\n\n
[
(x + y)(\\bar{x} + \\bar{z})
]<\/p>\n\n\n\n
\n\n\n\nConvert to Canonical (\u03a3m) Form<\/strong><\/h4>\n\n\n\n
x<\/th> y<\/th> z<\/th> F<\/th><\/tr><\/thead> 0<\/td> 0<\/td> 0<\/td> 0<\/td><\/tr> 0<\/td> 0<\/td> 1<\/td> 0<\/td><\/tr> 0<\/td> 1<\/td> 0<\/td> 0<\/td><\/tr> 0<\/td> 1<\/td> 1<\/td> 0<\/td><\/tr> 1<\/td> 0<\/td> 0<\/td> 1<\/td><\/tr> 1<\/td> 0<\/td> 1<\/td> 1<\/td><\/tr> 1<\/td> 1<\/td> 0<\/td> 1<\/td><\/tr> 1<\/td> 1<\/td> 1<\/td> 1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
F = \u03a3m(4,5,6,7)
]<\/p>\n\n\n\n
\n\n\n\nLogic Circuit for F<\/strong><\/h3>\n\n\n\n
\n
\n