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LU / Electrical Engineering / ENGE 201 / List the rules of simplification.

List the rules of simplification.

List the rules of simplification.

Description

.lst-kix_pn13t52ma58g-1 > li{counter-increment:lst-ctn-kix_pn13t52ma58g-1}.lst-kix_pn13t52ma58g-8 > li:before{content:"" counter(lst-ctn-kix_pn13t52ma58g-8,lower-roman) ". "}.lst-kix_pn13t52ma58g-7 > li:before{content:"" counter(lst-ctn-kix_pn13t52ma58g-7,lower-latin) ". "}.lst-kix_9e7a1yx6bnzv-1 > li{counter-increment:lst-ctn-kix_9e7a1yx6bnzv-1}.lst-kix_qz1bezfsqjx6-3 > li{counter-increment:lst-ctn-kix_qz1bezfsqjx6-3}.lst-kix_hug4by3v2qvr-4 > li{counter-increment:lst-ctn-kix_hug4by3v2qvr-4}.lst-kix_pn13t52ma58g-1 > li:before{content:"" counter(lst-ctn-kix_pn13t52ma58g-1,lower-latin) ". "}.lst-kix_pn13t52ma58g-0 > li:before{content:"" counter(lst-ctn-kix_pn13t52ma58g-0,decimal) ". "}.lst-kix_pn13t52ma58g-2 > li:before{content:"" counter(lst-ctn-kix_pn13t52ma58g-2,lower-roman) ". "}ol.lst-kix_v4lvk28c783l-4.start{counter-reset:lst-ctn-kix_v4lvk28c783l-4 0}.lst-kix_pn13t52ma58g-3 > li:before{content:"" counter(lst-ctn-kix_pn13t52ma58g-3,decimal) ". "}.lst-kix_qz1bezfsqjx6-5 > li{counter-increment:lst-ctn-kix_qz1bezfsqjx6-5}.lst-kix_hug4by3v2qvr-6 > li{counter-increment:lst-ctn-kix_hug4by3v2qvr-6}.lst-kix_pn13t52ma58g-5 > li:before{content:"" counter(lst-ctn-kix_pn13t52ma58g-5,lower-roman) ". "}.lst-kix_pn13t52ma58g-4 > li:before{content:"" counter(lst-ctn-kix_pn13t52ma58g-4,lower-latin) ". "}.lst-kix_pn13t52ma58g-6 > li:before{content:"" counter(lst-ctn-kix_pn13t52ma58g-6,decimal) ". "}.lst-kix_v4lvk28c783l-0 > li:before{content:"" counter(lst-ctn-kix_v4lvk28c783l-0,decimal) ". "}.lst-kix_v4lvk28c783l-3 > li:before{content:"" counter(lst-ctn-kix_v4lvk28c783l-3,decimal) ". "}ol.lst-kix_hug4by3v2qvr-4.start{counter-reset:lst-ctn-kix_hug4by3v2qvr-4 0}.lst-kix_v4lvk28c783l-2 > li:before{content:"" counter(lst-ctn-kix_v4lvk28c783l-2,lower-roman) ". "}.lst-kix_v4lvk28c783l-4 > li:before{content:"" counter(lst-ctn-kix_v4lvk28c783l-4,lower-latin) ". "}.lst-kix_idylzznl3nf9-0 > li:before{content:"- "}.lst-kix_idylzznl3nf9-2 > li:before{content:"- "}.lst-kix_v4lvk28c783l-1 > li:before{content:"" counter(lst-ctn-kix_v4lvk28c783l-1,lower-latin) ". "}.lst-kix_v4lvk28c783l-5 > li:before{content:"" counter(lst-ctn-kix_v4lvk28c783l-5,lower-roman) ". "}ol.lst-kix_qz1bezfsqjx6-5.start{counter-reset:lst-ctn-kix_qz1bezfsqjx6-5 0}.lst-kix_idylzznl3nf9-1 > li:before{content:"- "}ol.lst-kix_9e7a1yx6bnzv-5.start{counter-reset:lst-ctn-kix_9e7a1yx6bnzv-5 0}.lst-kix_9e7a1yx6bnzv-3 > li{counter-increment:lst-ctn-kix_9e7a1yx6bnzv-3}.lst-kix_gdpxxxlm7629-3 > li:before{content:"- "}ol.lst-kix_pn13t52ma58g-3.start{counter-reset:lst-ctn-kix_pn13t52ma58g-3 0}ol.lst-kix_v4lvk28c783l-3.start{counter-reset:lst-ctn-kix_v4lvk28c783l-3 0}.lst-kix_gdpxxxlm7629-2 > li:before{content:"- "}ol.lst-kix_qz1bezfsqjx6-4.start{counter-reset:lst-ctn-kix_qz1bezfsqjx6-4 0}.lst-kix_gdpxxxlm7629-1 > li:before{content:"- "}.lst-kix_gdpxxxlm7629-0 > li:before{content:"- "}.lst-kix_hug4by3v2qvr-8 > li{counter-increment:lst-ctn-kix_hug4by3v2qvr-8}ul.lst-kix_9unqz3b5jsdk-6{list-style-type:none}.lst-kix_qz1bezfsqjx6-7 > li{counter-increment:lst-ctn-kix_qz1bezfsqjx6-7}ul.lst-kix_9unqz3b5jsdk-7{list-style-type:none}ul.lst-kix_9unqz3b5jsdk-8{list-style-type:none}.lst-kix_pn13t52ma58g-5 > li{counter-increment:lst-ctn-kix_pn13t52ma58g-5}.lst-kix_v4lvk28c783l-8 > li{counter-increment:lst-ctn-kix_v4lvk28c783l-8}ol.lst-kix_pn13t52ma58g-4.start{counter-reset:lst-ctn-kix_pn13t52ma58g-4 0}.lst-kix_9e7a1yx6bnzv-7 > li:before{content:"" counter(lst-ctn-kix_9e7a1yx6bnzv-7,lower-latin) ". "}.lst-kix_9e7a1yx6bnzv-6 > li:before{content:"" counter(lst-ctn-kix_9e7a1yx6bnzv-6,decimal) ". "}.lst-kix_9e7a1yx6bnzv-8 > li:before{content:"" counter(lst-ctn-kix_9e7a1yx6bnzv-8,lower-roman) ". "}ul.lst-kix_9unqz3b5jsdk-0{list-style-type:none}ul.lst-kix_9unqz3b5jsdk-1{list-style-type:none}ul.lst-kix_9unqz3b5jsdk-2{list-style-type:none}ul.lst-kix_9unqz3b5jsdk-3{list-style-type:none}ul.lst-kix_9unqz3b5jsdk-4{list-style-type:none}ul.lst-kix_9unqz3b5jsdk-5{list-style-type:none}.lst-kix_9e7a1yx6bnzv-3 > li:before{content:"" counter(lst-ctn-kix_9e7a1yx6bnzv-3,decimal) ". "}.lst-kix_9e7a1yx6bnzv-2 > li:before{content:"" counter(lst-ctn-kix_9e7a1yx6bnzv-2,lower-roman) ". "}.lst-kix_9e7a1yx6bnzv-4 > li:before{content:"" counter(lst-ctn-kix_9e7a1yx6bnzv-4,lower-latin) ". "}.lst-kix_9e7a1yx6bnzv-1 > li:before{content:"" counter(lst-ctn-kix_9e7a1yx6bnzv-1,lower-latin) ". "}.lst-kix_9e7a1yx6bnzv-5 > li:before{content:"" counter(lst-ctn-kix_9e7a1yx6bnzv-5,lower-roman) ". "}.lst-kix_qz1bezfsqjx6-1 > li{counter-increment:lst-ctn-kix_qz1bezfsqjx6-1}.lst-kix_hug4by3v2qvr-2 > li{counter-increment:lst-ctn-kix_hug4by3v2qvr-2}.lst-kix_4qfin4iiad4a-5 > li:before{content:"- "}.lst-kix_9unqz3b5jsdk-8 > li:before{content:"- "}.lst-kix_pn13t52ma58g-7 > li{counter-increment:lst-ctn-kix_pn13t52ma58g-7}.lst-kix_v4lvk28c783l-5 > li{counter-increment:lst-ctn-kix_v4lvk28c783l-5}ul.lst-kix_1jc9awxi2awj-0{list-style-type:none}ol.lst-kix_pn13t52ma58g-5.start{counter-reset:lst-ctn-kix_pn13t52ma58g-5 0}ul.lst-kix_1jc9awxi2awj-4{list-style-type:none}ul.lst-kix_1jc9awxi2awj-3{list-style-type:none}ol.lst-kix_v4lvk28c783l-8.start{counter-reset:lst-ctn-kix_v4lvk28c783l-8 0}ul.lst-kix_1jc9awxi2awj-2{list-style-type:none}.lst-kix_9e7a1yx6bnzv-0 > li:before{content:"" counter(lst-ctn-kix_9e7a1yx6bnzv-0,decimal) ". "}.lst-kix_9unqz3b5jsdk-4 > li:before{content:"- "}ul.lst-kix_1jc9awxi2awj-1{list-style-type:none}ol.lst-kix_v4lvk28c783l-5.start{counter-reset:lst-ctn-kix_v4lvk28c783l-5 0}ul.lst-kix_1jc9awxi2awj-8{list-style-type:none}.lst-kix_4qfin4iiad4a-3 > li:before{content:"- "}ul.lst-kix_3mv8jigp030u-7{list-style-type:none}ul.lst-kix_1jc9awxi2awj-7{list-style-type:none}ul.lst-kix_3mv8jigp030u-8{list-style-type:none}ul.lst-kix_1jc9awxi2awj-6{list-style-type:none}ul.lst-kix_3mv8jigp030u-5{list-style-type:none}ul.lst-kix_1jc9awxi2awj-5{list-style-type:none}ul.lst-kix_3mv8jigp030u-6{list-style-type:none}ul.lst-kix_3mv8jigp030u-3{list-style-type:none}ul.lst-kix_3mv8jigp030u-4{list-style-type:none}ul.lst-kix_3mv8jigp030u-1{list-style-type:none}ul.lst-kix_3mv8jigp030u-2{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-2{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-1{list-style-type:none}ul.lst-kix_3mv8jigp030u-0{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-0{list-style-type:none}.lst-kix_9unqz3b5jsdk-6 > li:before{content:"- "}.lst-kix_4qfin4iiad4a-7 > li:before{content:"- "}ol.lst-kix_pn13t52ma58g-8.start{counter-reset:lst-ctn-kix_pn13t52ma58g-8 0}ol.lst-kix_9e7a1yx6bnzv-4.start{counter-reset:lst-ctn-kix_9e7a1yx6bnzv-4 0}ol.lst-kix_qz1bezfsqjx6-6.start{counter-reset:lst-ctn-kix_qz1bezfsqjx6-6 0}ul.lst-kix_gdpxxxlm7629-0{list-style-type:none}ul.lst-kix_gdpxxxlm7629-2{list-style-type:none}ul.lst-kix_gdpxxxlm7629-1{list-style-type:none}ul.lst-kix_gdpxxxlm7629-4{list-style-type:none}ul.lst-kix_gdpxxxlm7629-3{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-6{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-5{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-4{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-3{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-8{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-7{list-style-type:none}.lst-kix_9unqz3b5jsdk-0 > li:before{content:"- "}.lst-kix_9unqz3b5jsdk-2 > li:before{content:"- "}.lst-kix_3mv8jigp030u-3 > li:before{content:"- "}.lst-kix_4qfin4iiad4a-1 > li:before{content:"- "}ul.lst-kix_gdpxxxlm7629-6{list-style-type:none}.lst-kix_3mv8jigp030u-1 > li:before{content:"- "}ul.lst-kix_gdpxxxlm7629-5{list-style-type:none}ul.lst-kix_gdpxxxlm7629-8{list-style-type:none}.lst-kix_v4lvk28c783l-3 > li{counter-increment:lst-ctn-kix_v4lvk28c783l-3}ul.lst-kix_gdpxxxlm7629-7{list-style-type:none}.lst-kix_qz1bezfsqjx6-8 > li{counter-increment:lst-ctn-kix_qz1bezfsqjx6-8}ol.lst-kix_v4lvk28c783l-7{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-6.start{counter-reset:lst-ctn-kix_9e7a1yx6bnzv-6 0}.lst-kix_idylzznl3nf9-8 > li:before{content:"- "}ol.lst-kix_v4lvk28c783l-8{list-style-type:none}.lst-kix_gdpxxxlm7629-5 > li:before{content:"- "}.lst-kix_4j0zpr4bfnje-3 > li:before{content:"- "}.lst-kix_4j0zpr4bfnje-5 > li:before{content:"- "}ol.lst-kix_v4lvk28c783l-5{list-style-type:none}ol.lst-kix_v4lvk28c783l-6{list-style-type:none}ol.lst-kix_v4lvk28c783l-3{list-style-type:none}ol.lst-kix_v4lvk28c783l-4{list-style-type:none}.lst-kix_qz1bezfsqjx6-0 > li:before{content:"" counter(lst-ctn-kix_qz1bezfsqjx6-0,decimal) ". "}.lst-kix_qz1bezfsqjx6-2 > li:before{content:"" counter(lst-ctn-kix_qz1bezfsqjx6-2,lower-roman) ". "}.lst-kix_v4lvk28c783l-6 > li:before{content:"" counter(lst-ctn-kix_v4lvk28c783l-6,decimal) ". "}.lst-kix_v4lvk28c783l-8 > li:before{content:"" counter(lst-ctn-kix_v4lvk28c783l-8,lower-roman) ". "}.lst-kix_idylzznl3nf9-4 > li:before{content:"- "}.lst-kix_gdpxxxlm7629-7 > li:before{content:"- "}.lst-kix_qz1bezfsqjx6-4 > li:before{content:"" counter(lst-ctn-kix_qz1bezfsqjx6-4,lower-latin) ". "}.lst-kix_qz1bezfsqjx6-6 > li:before{content:"" counter(lst-ctn-kix_qz1bezfsqjx6-6,decimal) ". "}ol.lst-kix_v4lvk28c783l-7.start{counter-reset:lst-ctn-kix_v4lvk28c783l-7 0}ol.lst-kix_hug4by3v2qvr-5.start{counter-reset:lst-ctn-kix_hug4by3v2qvr-5 0}.lst-kix_9b6sj2nivnnn-4 > li:before{content:"- "}.lst-kix_9b6sj2nivnnn-8 > li:before{content:"- "}ol.lst-kix_v4lvk28c783l-1{list-style-type:none}.lst-kix_9e7a1yx6bnzv-8 > li{counter-increment:lst-ctn-kix_9e7a1yx6bnzv-8}ol.lst-kix_v4lvk28c783l-2{list-style-type:none}.lst-kix_idylzznl3nf9-6 > li:before{content:"- "}ol.lst-kix_v4lvk28c783l-0{list-style-type:none}.lst-kix_4j0zpr4bfnje-7 > li:before{content:"- "}.lst-kix_9b6sj2nivnnn-6 > li:before{content:"- "}ol.lst-kix_9e7a1yx6bnzv-7.start{counter-reset:lst-ctn-kix_9e7a1yx6bnzv-7 0}.lst-kix_pn13t52ma58g-0 > li{counter-increment:lst-ctn-kix_pn13t52ma58g-0}.lst-kix_9b6sj2nivnnn-0 > li:before{content:"- "}.lst-kix_1jc9awxi2awj-3 > li:before{content:"- "}.lst-kix_qz1bezfsqjx6-8 > li:before{content:"" counter(lst-ctn-kix_qz1bezfsqjx6-8,lower-roman) ". "}ol.lst-kix_qz1bezfsqjx6-8{list-style-type:none}.lst-kix_9e7a1yx6bnzv-2 > li{counter-increment:lst-ctn-kix_9e7a1yx6bnzv-2}ol.lst-kix_qz1bezfsqjx6-6{list-style-type:none}ol.lst-kix_qz1bezfsqjx6-7{list-style-type:none}ol.lst-kix_qz1bezfsqjx6-4{list-style-type:none}ol.lst-kix_qz1bezfsqjx6-5{list-style-type:none}.lst-kix_9b6sj2nivnnn-2 > li:before{content:"- "}.lst-kix_pn13t52ma58g-6 > li{counter-increment:lst-ctn-kix_pn13t52ma58g-6}.lst-kix_1jc9awxi2awj-1 > li:before{content:"- "}.lst-kix_v4lvk28c783l-4 > li{counter-increment:lst-ctn-kix_v4lvk28c783l-4}ol.lst-kix_qz1bezfsqjx6-2{list-style-type:none}ol.lst-kix_pn13t52ma58g-7.start{counter-reset:lst-ctn-kix_pn13t52ma58g-7 0}ol.lst-kix_qz1bezfsqjx6-3{list-style-type:none}ol.lst-kix_qz1bezfsqjx6-0{list-style-type:none}ol.lst-kix_qz1bezfsqjx6-1{list-style-type:none}ol.lst-kix_v4lvk28c783l-6.start{counter-reset:lst-ctn-kix_v4lvk28c783l-6 0}.lst-kix_1jc9awxi2awj-7 > li:before{content:"- "}ol.lst-kix_qz1bezfsqjx6-7.start{counter-reset:lst-ctn-kix_qz1bezfsqjx6-7 0}.lst-kix_4j0zpr4bfnje-1 > li:before{content:"- "}.lst-kix_1jc9awxi2awj-5 > li:before{content:"- "}ol.lst-kix_hug4by3v2qvr-6.start{counter-reset:lst-ctn-kix_hug4by3v2qvr-6 0}.lst-kix_hug4by3v2qvr-5 > li{counter-increment:lst-ctn-kix_hug4by3v2qvr-5}.lst-kix_qz1bezfsqjx6-4 > li{counter-increment:lst-ctn-kix_qz1bezfsqjx6-4}.lst-kix_pn13t52ma58g-2 > li{counter-increment:lst-ctn-kix_pn13t52ma58g-2}ol.lst-kix_pn13t52ma58g-3{list-style-type:none}ol.lst-kix_pn13t52ma58g-2{list-style-type:none}ol.lst-kix_pn13t52ma58g-1{list-style-type:none}ol.lst-kix_hug4by3v2qvr-2.start{counter-reset:lst-ctn-kix_hug4by3v2qvr-2 0}ol.lst-kix_pn13t52ma58g-0{list-style-type:none}ol.lst-kix_pn13t52ma58g-7{list-style-type:none}ol.lst-kix_pn13t52ma58g-6{list-style-type:none}ol.lst-kix_pn13t52ma58g-5{list-style-type:none}ol.lst-kix_pn13t52ma58g-4{list-style-type:none}ol.lst-kix_hug4by3v2qvr-7.start{counter-reset:lst-ctn-kix_hug4by3v2qvr-7 0}.lst-kix_qz1bezfsqjx6-2 > li{counter-increment:lst-ctn-kix_qz1bezfsqjx6-2}.lst-kix_hug4by3v2qvr-3 > li{counter-increment:lst-ctn-kix_hug4by3v2qvr-3}ol.lst-kix_pn13t52ma58g-8{list-style-type:none}ol.lst-kix_hug4by3v2qvr-8{list-style-type:none}ol.lst-kix_qz1bezfsqjx6-8.start{counter-reset:lst-ctn-kix_qz1bezfsqjx6-8 0}ol.lst-kix_pn13t52ma58g-6.start{counter-reset:lst-ctn-kix_pn13t52ma58g-6 0}ol.lst-kix_9e7a1yx6bnzv-2.start{counter-reset:lst-ctn-kix_9e7a1yx6bnzv-2 0}ul.lst-kix_4j0zpr4bfnje-0{list-style-type:none}ol.lst-kix_hug4by3v2qvr-3{list-style-type:none}ul.lst-kix_4j0zpr4bfnje-1{list-style-type:none}ol.lst-kix_hug4by3v2qvr-2{list-style-type:none}ol.lst-kix_hug4by3v2qvr-1{list-style-type:none}ol.lst-kix_hug4by3v2qvr-0{list-style-type:none}ul.lst-kix_4j0zpr4bfnje-4{list-style-type:none}ol.lst-kix_hug4by3v2qvr-7{list-style-type:none}ul.lst-kix_4j0zpr4bfnje-5{list-style-type:none}ol.lst-kix_hug4by3v2qvr-6{list-style-type:none}ol.lst-kix_v4lvk28c783l-1.start{counter-reset:lst-ctn-kix_v4lvk28c783l-1 0}ul.lst-kix_4j0zpr4bfnje-2{list-style-type:none}ol.lst-kix_hug4by3v2qvr-5{list-style-type:none}ul.lst-kix_4j0zpr4bfnje-3{list-style-type:none}ol.lst-kix_hug4by3v2qvr-4{list-style-type:none}ol.lst-kix_9e7a1yx6bnzv-8.start{counter-reset:lst-ctn-kix_9e7a1yx6bnzv-8 0}ul.lst-kix_4j0zpr4bfnje-8{list-style-type:none}ul.lst-kix_4j0zpr4bfnje-6{list-style-type:none}.lst-kix_9e7a1yx6bnzv-0 > li{counter-increment:lst-ctn-kix_9e7a1yx6bnzv-0}ul.lst-kix_4j0zpr4bfnje-7{list-style-type:none}ol.lst-kix_qz1bezfsqjx6-2.start{counter-reset:lst-ctn-kix_qz1bezfsqjx6-2 0}.lst-kix_v4lvk28c783l-0 > li{counter-increment:lst-ctn-kix_v4lvk28c783l-0}.lst-kix_pn13t52ma58g-4 > li{counter-increment:lst-ctn-kix_pn13t52ma58g-4}.lst-kix_v4lvk28c783l-2 > li{counter-increment:lst-ctn-kix_v4lvk28c783l-2}ol.lst-kix_hug4by3v2qvr-8.start{counter-reset:lst-ctn-kix_hug4by3v2qvr-8 0}.lst-kix_3mv8jigp030u-4 > li:before{content:"- "}.lst-kix_9e7a1yx6bnzv-4 > li{counter-increment:lst-ctn-kix_9e7a1yx6bnzv-4}.lst-kix_3mv8jigp030u-5 > li:before{content:"- "}.lst-kix_3mv8jigp030u-7 > li:before{content:"- "}.lst-kix_3mv8jigp030u-6 > li:before{content:"- "}.lst-kix_3mv8jigp030u-8 > li:before{content:"- "}.lst-kix_hug4by3v2qvr-1 > li:before{content:"" counter(lst-ctn-kix_hug4by3v2qvr-1,lower-latin) ". "}.lst-kix_hug4by3v2qvr-2 > li:before{content:"" counter(lst-ctn-kix_hug4by3v2qvr-2,lower-roman) ". "}.lst-kix_hug4by3v2qvr-3 > li:before{content:"" counter(lst-ctn-kix_hug4by3v2qvr-3,decimal) ". "}ol.lst-kix_qz1bezfsqjx6-3.start{counter-reset:lst-ctn-kix_qz1bezfsqjx6-3 0}.lst-kix_hug4by3v2qvr-5 > li:before{content:"" counter(lst-ctn-kix_hug4by3v2qvr-5,lower-roman) ". "}.lst-kix_hug4by3v2qvr-4 > li:before{content:"" counter(lst-ctn-kix_hug4by3v2qvr-4,lower-latin) ". "}.lst-kix_hug4by3v2qvr-6 > li:before{content:"" counter(lst-ctn-kix_hug4by3v2qvr-6,decimal) ". "}.lst-kix_9e7a1yx6bnzv-7 > li{counter-increment:lst-ctn-kix_9e7a1yx6bnzv-7}.lst-kix_hug4by3v2qvr-8 > li:before{content:"" counter(lst-ctn-kix_hug4by3v2qvr-8,lower-roman) ". "}.lst-kix_hug4by3v2qvr-7 > li:before{content:"" counter(lst-ctn-kix_hug4by3v2qvr-7,lower-latin) ". "}ol.lst-kix_hug4by3v2qvr-3.start{counter-reset:lst-ctn-kix_hug4by3v2qvr-3 0}ol.lst-kix_9e7a1yx6bnzv-3.start{counter-reset:lst-ctn-kix_9e7a1yx6bnzv-3 0}ul.lst-kix_4qfin4iiad4a-2{list-style-type:none}ul.lst-kix_4qfin4iiad4a-1{list-style-type:none}ul.lst-kix_4qfin4iiad4a-0{list-style-type:none}.lst-kix_4qfin4iiad4a-4 > li:before{content:"- "}.lst-kix_4qfin4iiad4a-6 > li:before{content:"- "}.lst-kix_9e7a1yx6bnzv-6 > li{counter-increment:lst-ctn-kix_9e7a1yx6bnzv-6}ol.lst-kix_9e7a1yx6bnzv-1.start{counter-reset:lst-ctn-kix_9e7a1yx6bnzv-1 0}.lst-kix_4qfin4iiad4a-2 > li:before{content:"- "}ul.lst-kix_4qfin4iiad4a-8{list-style-type:none}ul.lst-kix_4qfin4iiad4a-7{list-style-type:none}ul.lst-kix_4qfin4iiad4a-6{list-style-type:none}ul.lst-kix_4qfin4iiad4a-5{list-style-type:none}ul.lst-kix_4qfin4iiad4a-4{list-style-type:none}ul.lst-kix_4qfin4iiad4a-3{list-style-type:none}.lst-kix_9unqz3b5jsdk-3 > li:before{content:"- "}.lst-kix_pn13t52ma58g-8 > li{counter-increment:lst-ctn-kix_pn13t52ma58g-8}.lst-kix_9unqz3b5jsdk-5 > li:before{content:"- "}ol.lst-kix_v4lvk28c783l-2.start{counter-reset:lst-ctn-kix_v4lvk28c783l-2 0}.lst-kix_4qfin4iiad4a-8 > li:before{content:"- "}ul.lst-kix_idylzznl3nf9-7{list-style-type:none}.lst-kix_9unqz3b5jsdk-7 > li:before{content:"- "}ul.lst-kix_idylzznl3nf9-8{list-style-type:none}.lst-kix_hug4by3v2qvr-0 > li:before{content:"" counter(lst-ctn-kix_hug4by3v2qvr-0,decimal) ". "}.lst-kix_v4lvk28c783l-6 > li{counter-increment:lst-ctn-kix_v4lvk28c783l-6}ol.lst-kix_pn13t52ma58g-2.start{counter-reset:lst-ctn-kix_pn13t52ma58g-2 0}.lst-kix_hug4by3v2qvr-0 > li{counter-increment:lst-ctn-kix_hug4by3v2qvr-0}ul.lst-kix_9b6sj2nivnnn-3{list-style-type:none}ul.lst-kix_9b6sj2nivnnn-2{list-style-type:none}ul.lst-kix_9b6sj2nivnnn-1{list-style-type:none}ul.lst-kix_9b6sj2nivnnn-0{list-style-type:none}ul.lst-kix_9b6sj2nivnnn-7{list-style-type:none}ul.lst-kix_9b6sj2nivnnn-6{list-style-type:none}ul.lst-kix_9b6sj2nivnnn-5{list-style-type:none}.lst-kix_3mv8jigp030u-2 > li:before{content:"- "}ul.lst-kix_9b6sj2nivnnn-4{list-style-type:none}.lst-kix_9unqz3b5jsdk-1 > li:before{content:"- "}.lst-kix_4qfin4iiad4a-0 > li:before{content:"- "}ul.lst-kix_9b6sj2nivnnn-8{list-style-type:none}.lst-kix_3mv8jigp030u-0 > li:before{content:"- "}.lst-kix_gdpxxxlm7629-4 > li:before{content:"- "}ol.lst-kix_hug4by3v2qvr-1.start{counter-reset:lst-ctn-kix_hug4by3v2qvr-1 0}.lst-kix_idylzznl3nf9-5 > li:before{content:"- "}.lst-kix_gdpxxxlm7629-6 > li:before{content:"- "}.lst-kix_4j0zpr4bfnje-2 > li:before{content:"- "}.lst-kix_4j0zpr4bfnje-6 > li:before{content:"- "}.lst-kix_qz1bezfsqjx6-1 > li:before{content:"" counter(lst-ctn-kix_qz1bezfsqjx6-1,lower-latin) ". "}.lst-kix_v4lvk28c783l-7 > li:before{content:"" counter(lst-ctn-kix_v4lvk28c783l-7,lower-latin) ". "}.lst-kix_idylzznl3nf9-3 > li:before{content:"- "}ol.lst-kix_v4lvk28c783l-0.start{counter-reset:lst-ctn-kix_v4lvk28c783l-0 0}.lst-kix_gdpxxxlm7629-8 > li:before{content:"- "}.lst-kix_4j0zpr4bfnje-4 > li:before{content:"- "}.lst-kix_qz1bezfsqjx6-5 > li:before{content:"" counter(lst-ctn-kix_qz1bezfsqjx6-5,lower-roman) ". "}.lst-kix_hug4by3v2qvr-1 > li{counter-increment:lst-ctn-kix_hug4by3v2qvr-1}.lst-kix_9b6sj2nivnnn-5 > li:before{content:"- "}.lst-kix_9b6sj2nivnnn-7 > li:before{content:"- "}.lst-kix_qz1bezfsqjx6-3 > li:before{content:"" counter(lst-ctn-kix_qz1bezfsqjx6-3,decimal) ". "}.lst-kix_qz1bezfsqjx6-7 > li:before{content:"" counter(lst-ctn-kix_qz1bezfsqjx6-7,lower-latin) ". "}ol.lst-kix_pn13t52ma58g-0.start{counter-reset:lst-ctn-kix_pn13t52ma58g-0 0}ol.lst-kix_qz1bezfsqjx6-1.start{counter-reset:lst-ctn-kix_qz1bezfsqjx6-1 0}.lst-kix_qz1bezfsqjx6-6 > li{counter-increment:lst-ctn-kix_qz1bezfsqjx6-6}.lst-kix_qz1bezfsqjx6-0 > li{counter-increment:lst-ctn-kix_qz1bezfsqjx6-0}.lst-kix_hug4by3v2qvr-7 > li{counter-increment:lst-ctn-kix_hug4by3v2qvr-7}.lst-kix_idylzznl3nf9-7 > li:before{content:"- "}.lst-kix_4j0zpr4bfnje-8 > li:before{content:"- "}ul.lst-kix_idylzznl3nf9-3{list-style-type:none}ul.lst-kix_idylzznl3nf9-4{list-style-type:none}ul.lst-kix_idylzznl3nf9-5{list-style-type:none}.lst-kix_1jc9awxi2awj-2 > li:before{content:"- "}.lst-kix_1jc9awxi2awj-4 > li:before{content:"- "}ul.lst-kix_idylzznl3nf9-6{list-style-type:none}ul.lst-kix_idylzznl3nf9-0{list-style-type:none}ul.lst-kix_idylzznl3nf9-1{list-style-type:none}.lst-kix_9e7a1yx6bnzv-5 > li{counter-increment:lst-ctn-kix_9e7a1yx6bnzv-5}ul.lst-kix_idylzznl3nf9-2{list-style-type:none}.lst-kix_9b6sj2nivnnn-1 > li:before{content:"- "}.lst-kix_9b6sj2nivnnn-3 > li:before{content:"- "}.lst-kix_pn13t52ma58g-3 > li{counter-increment:lst-ctn-kix_pn13t52ma58g-3}.lst-kix_1jc9awxi2awj-0 > li:before{content:"- "}.lst-kix_1jc9awxi2awj-8 > li:before{content:"- "}.lst-kix_v4lvk28c783l-1 > li{counter-increment:lst-ctn-kix_v4lvk28c783l-1}ol.lst-kix_hug4by3v2qvr-0.start{counter-reset:lst-ctn-kix_hug4by3v2qvr-0 0}.lst-kix_v4lvk28c783l-7 > li{counter-increment:lst-ctn-kix_v4lvk28c783l-7}ol.lst-kix_qz1bezfsqjx6-0.start{counter-reset:lst-ctn-kix_qz1bezfsqjx6-0 0}ol.lst-kix_pn13t52ma58g-1.start{counter-reset:lst-ctn-kix_pn13t52ma58g-1 0}.lst-kix_1jc9awxi2awj-6 > li:before{content:"- "}ol.lst-kix_9e7a1yx6bnzv-0.start{counter-reset:lst-ctn-kix_9e7a1yx6bnzv-0 0}.lst-kix_4j0zpr4bfnje-0 > li:before{content:"- "}

ENGE 201

  • Theories of Boolean algebra are used to minimize a boolean expression to reduce the number of logic gates in a network
  • Make sure you can make a boolean expression from a truth table

  • Theorems!

X.x = 0                x.y - x + y                all are on page 99Don't forget about the age old question of The most common arrangement of protein coding genes is?

X + x = 1        x + y = x.y

X (+) x = 1        x + xy = xWe also discuss several other topics like What is the 2nd order kinetics?
If you want to learn more check out Explain what the chain rule equation is.
Don't forget about the age old question of Why is adjusting entries important?

(x + y)(x + z) = x + yz

X.x + x.y + x.7 + y.z

X + xy + xz + yz

X + xz + yzWe also discuss several other topics like What is the capital of Australia?

X + yz

X + xy = x + y and x+ xy = x + y and x + xy = x + yWe also discuss several other topics like What refers to computer algorithms that analyze info to discover previously unknown and potentially useful information including relationships and patterns?

Simplification of combinational logic circuits using Boolean algebra

  • 1rst step = write the equation
  • Apply laws to decrease number of terms and variables
  • Remove parenthesis / brackets

Example:

AB + BC (B + C)

AB + B.B.C + B.C.C                distribute

AB + BC + BC                AA = A

AB + BS                        A + A = A                SOP form

B (A + C)                        factor                        POS form

Rules of Simplification

  1. Groups must be made from same variable

Example: (1 and 1), not (1 and 0)

  1. Groups may be horizontal or vertical but not diagonal
  2. The number of cells in a group must be a power of 2
  3. Each group should be as large as possible resulting in as few groups as possible
  4. Each will containing a 1 must be part of a group if possible
  5. Groups may overlap

Multiple groups

  • Each groups must have at least one cell that does not belong to any other group
  1. Groups may wrap around the table

Example: this is one groups

Example: all 4 corners count

Complete Simplification Process

  • When a variable appears in both complemented and truth form, it is eliminated

Example:

 x = ABCD + ACD + BD

**For every group, there’s a term**

ENGE 201

 

y

minterm

maxterm

ABCD + ABCD + ABCD + ABCD + ABCD

(A + B C D)(A + B + C +D)(A + B + C + D)

ABCD + ABCD + ABCD + ABCD +ABCD

ABCD + AB(CD + CD) + AB (CD + CD)

ABCD + (AB + AB)(CD + CD)

**Practice Simplifying**

Karnaugh maps

  • Can be used for many variables but typically limited to 5 or 6

Construction

  • Each cell represents a line in the truth table (in TITLE)
  • The coordinates of any 2 adjacent cells differ by only one variable, that why you do back - skip

**Look at chart on page 109

  • When a letter is barred, that’s a 0 Example: A,B
  • When a letter is not barred, that’s a 1 Example: A,B

Example:

(A + B)(A + C)

AA + AB + AC + BC                        AA = A

A + AB + AC + BC                        A + AB = A

A + AC + BC                                A + AC = A

A + BC

Example:

ABC + ABC + ABC + ABC

BC (A + A) + ABC + ABC                A + A = 1

BC + ABC + ABC                        1A = A

B (C + AC) + ABC                        factor

B (C + A) + ABC                        A + AB = A + B rule

BC + BA + ABC                        distribute

B (C + A) + AVC                        factor

BC + A (B + C)                        A + AB = A + B rule

3C + AB + AC                        distribute

Example:

A + BC + AB                                breaking longest bar

(A + BC) (AB)                                A = A

(A + BC) (AB)                                distribute

AAB + BCAB                                AA = A, AA = 0

AB + 0

AB

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