“The Elements of Computing Systems

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);

The Correct Answer and Explanation is:

✅ Correct Answer (Mux8Way16.hdl Implementation):

hdlCopyEdit// 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
 *       c if sel == 010
 *       d if sel == 011
 *       e if sel == 100
 *       f if sel == 101
 *       g if sel == 110
 *       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);
}

📘 Explanation

The Mux8Way16 chip is a key component in digital circuit design. It selects one of eight 16-bit input buses (a through h) and outputs it to the 16-bit output bus out. The selection is based on a 3-bit input called sel.

Each possible value of sel represents a different input to choose:

• 000 selects a
• 001 selects b
• 010 selects c
• 011 selects d
• 100 selects e
• 101 selects f
• 110 selects g
• 111 selects h

To implement this, the design uses a hierarchy of multiplexors. First, it uses two Mux4Way16 chips:

• The first one takes inputs a, b, c, and d, and uses the first two bits of sel (sel[0..1]) to choose one of them. Its output is stored in muxAD.
• The second one takes inputs e, f, g, and h, also using sel[0..1], and outputs the selected value to muxEH.

These two intermediate outputs (muxAD and muxEH) are then fed into a single Mux16, which uses the third bit of sel (sel[2]) to choose between them. This effectively divides the selection into two stages:

1. Choose one of two groups (first four or last four) based on sel[2].
2. Choose one of four within that group based on sel[0..1].

This structured and modular approach simplifies complex selection logic using simpler components.