{"id":2978,"date":"2024-08-25T22:11:14","date_gmt":"2024-08-25T22:11:14","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2978"},"modified":"2024-08-25T22:11:14","modified_gmt":"2024-08-25T22:11:14","slug":"nand-and-and-gates","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/nand-and-and-gates\/","title":{"rendered":"Nand and AND Gates"},"content":{"rendered":"\n

The implementations of the NOT and BUF gates shown above illustrate an important point, which is that it is generally easier to implement an inverting function than its non-inverting equivalent. In the same way that a NOT is easier to implement than a BUF, a NAND is easier to implement than an AND, and a NOR is easier to implement than an OR. More significantly, inverting functions typically require fewer transistors and operate faster than their non-inverting counterparts. This can obviously be an important design consideration. Consider a 2-input NAND gate, which requires four transistors (Figure 10.23). (Note that a 3-input version could be constructed by adding an additional PMOS transistor in parallel with Tr1<\/sub>\u00a0and Tr2<\/sub>, and an additional NMOS transistor in series with Tr3<\/sub>\u00a0and Tr4<\/sub>.)<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 10.23<\/strong> CMOS implementation of a 2-input NAND gate<\/p>\n\n\n\n

When both\u00a0a<\/em>\u00a0and\u00a0b<\/em>\u00a0are presented with logic 1s, transistors Tr1<\/sub>\u00a0and Tr2<\/sub>\u00a0are turned OFF, transistors Tr3<\/sub>\u00a0and Tr4<\/sub>\u00a0are turned ON, and output\u00a0y<\/em>\u00a0is connected to logic 0 via Tr3<\/sub>\u00a0and Tr4<\/sub>. Any other combination of inputs results in one or both of Tr3<\/sub>\u00a0and Tr4<\/sub>\u00a0being turned OFF, one or both of Tr1<\/sub>\u00a0and Tr2<\/sub>\u00a0being turned ON, and output\u00a0y<\/em>\u00a0being connected to logic 1 via Tr1<\/sub>\u00a0and\/or Tr2<\/sub>. Once again, it may help to visualize the gate\u2019s operation in terms of switches rather than transistors (Figure 10.24).<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 10.24<\/strong> NAND gate\u2019s operation represented in terms of switches<\/p>\n\n\n\n

Now consider an AND gate. This is formed by inverting the output of a NAND with a NOT, which means that a 2-input AND requires six transistors (Figure 10.25).<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 10.25<\/strong> CMOS implementation of a 2-input AND gate<\/p>\n","protected":false},"excerpt":{"rendered":"

The implementations of the NOT and BUF gates shown above illustrate an important point, which is that it is generally easier to implement an inverting function than its non-inverting equivalent. In the same way that a NOT is easier to implement than a BUF, a NAND is easier to implement than an AND, and a […]<\/p>\n","protected":false},"author":1,"featured_media":2976,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[417],"tags":[],"class_list":["post-2978","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-digital-electronics"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/circuit.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2978","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=2978"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2978\/revisions"}],"predecessor-version":[{"id":2979,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2978\/revisions\/2979"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2976"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}