{"id":37347,"date":"2025-06-25T17:16:23","date_gmt":"2025-06-25T17:16:23","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=37347"},"modified":"2025-06-26T07:54:24","modified_gmt":"2025-06-26T07:54:24","slug":"the-elements-of-computing-systems","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-elements-of-computing-systems\/","title":{"rendered":"The Elements of Computing Systems"},"content":{"rendered":"\n

Mux8Way16.hdl – Notepad File Edit Format View Help \/\/ This file is part of www.nand2tetris.org \/\/ and the book “The Elements of Computing Systems” \/\/ by Nisan and Schocken, MIT Press. \/\/ File name: projects\/01\/Mux8Way16.hdl \/** 8-way 16-bit multiplexor: * out = a if sel == 000 * * * b if sel == 001 etc. h if sel == 111 *\/ CHIP Mux8Way16 { IN a[16], b[16], c[16], d[16], e[16], f[16], g[16], h[16], sel[3]; OUT out[16]; } PARTS: Mux4Way16(a=a, b=b, c=c, d=d, sel=sel[0..1], out=muxAD); Mux4Way16(a=e, b=f, c=g, d=h, sel=sel[0..1], out=muxEH); Mux16(a=muxAD, b=muxEH, sel=sel[2], out=out); }<\/p>\n\n\n\n

Mux8Way16.hdl - Notepad File Edit Format View Help \/\/ This file is part of www.nand2tetris.org \/\/ and the book \"The Elements of Computing Systems\" \/\/ by Nisan and Schocken, MIT Press. \/\/ File name: projects\/01\/Mux8Way16.hdl \/** 8-way 16-bit multiplexor: * out = a if sel == 000 * * * b if sel == 001 etc. h if sel == 111 *\/ CHIP Mux8Way16 { IN a[16], b[16], c[16], d[16], e[16], f[16], g[16], h[16], sel[3]; OUT out[16]; } PARTS: Mux4Way16(a=a, b=b, c=c, d=d, sel=sel[0..1], out=muxAD); Mux4Way16(a=e, b=f, c=g, d=h, sel=sel[0..1], out=muxEH); Mux16(a=muxAD, b=muxEH, sel=sel[2], out=out); }<\/pre>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Correct Answer: The given HDL code for Mux8Way16<\/code> is correct and implements an 8-way 16-bit multiplexor using two Mux4Way16<\/code> gates and one Mux16<\/code> gate.<\/strong><\/p>\n\n\n\n
\n\n\n\n
Explanation:<\/strong><\/p>\n\n\n\n
This Hardware Description Language (HDL) file defines a chip called Mux8Way16<\/code>, which is an 8-input, 16-bit-wide multiplexer. A multiplexer selects one of several input buses and forwards it to the output based on a selection signal. In this case, there are 8 input buses labeled a<\/code> through h<\/code>, each 16 bits wide. The sel<\/code> input is a 3-bit selection signal that determines which input gets passed to the output.<\/p>\n\n\n\n
Here is how the design works:<\/p>\n\n\n\n
    \n
  1. The 8 inputs are divided into two groups of four:\n
      \n
    • The first group includes a<\/code>, b<\/code>, c<\/code>, and d<\/code>.<\/li>\n\n\n\n
    • The second group includes e<\/code>, f<\/code>, g<\/code>, and h<\/code>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Two Mux4Way16<\/code> chips are used:\n
        \n
      • The first Mux4Way16<\/code> receives inputs a<\/code> to d<\/code> and selects one based on the lower two bits of sel<\/code> (sel[0..1]<\/code>). The output of this multiplexer is stored in a temporary wire named muxAD<\/code>.<\/li>\n\n\n\n
      • The second Mux4Way16<\/code> does the same for inputs e<\/code> to h<\/code>, and its output is stored in muxEH<\/code>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Finally, a regular Mux16<\/code> is used to choose between muxAD<\/code> and muxEH<\/code>. This selection is based on the most significant bit of sel<\/code> (sel[2]<\/code>).<\/li>\n<\/ol>\n\n\n\n
        The full selection process is as follows:<\/p>\n\n\n\n
          \n
        • If sel[2]<\/code> is 0, the output comes from the first group (a<\/code> to d<\/code>).<\/li>\n\n\n\n
        • If sel[2]<\/code> is 1, the output comes from the second group (e<\/code> to h<\/code>).<\/li>\n\n\n\n
        • Within each group, sel[1]<\/code> and sel[0]<\/code> determine which specific input is selected.<\/li>\n<\/ul>\n\n\n\n
          This modular approach makes the design readable, scalable, and easy to debug.<\/p>\n\n\n\n
          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
          Mux8Way16.hdl – Notepad File Edit Format View Help \/\/ This file is part of www.nand2tetris.org \/\/ and the book “The Elements of Computing Systems” \/\/ by Nisan and Schocken, MIT Press. \/\/ File name: projects\/01\/Mux8Way16.hdl \/** 8-way 16-bit multiplexor: * out = a if sel == 000 * * * b if sel == 001 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37347","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37347","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37347"}],"version-history":[{"count":2,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37347\/revisions"}],"predecessor-version":[{"id":38063,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37347\/revisions\/38063"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}