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); }

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: The given HDL code for Mux8Way16 is correct and implements an 8-way 16-bit multiplexor using two Mux4Way16 gates and one Mux16 gate.

Explanation:

This Hardware Description Language (HDL) file defines a chip called Mux8Way16, 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 through h, each 16 bits wide. The sel input is a 3-bit selection signal that determines which input gets passed to the output.

Here is how the design works:

1. The 8 inputs are divided into two groups of four:
   • The first group includes a, b, c, and d.
   • The second group includes e, f, g, and h.
2. Two Mux4Way16 chips are used:
   • The first Mux4Way16 receives inputs a to d and selects one based on the lower two bits of sel (sel[0..1]). The output of this multiplexer is stored in a temporary wire named muxAD.
   • The second Mux4Way16 does the same for inputs e to h, and its output is stored in muxEH.
3. Finally, a regular Mux16 is used to choose between muxAD and muxEH. This selection is based on the most significant bit of sel (sel[2]).

The full selection process is as follows:

• If sel[2] is 0, the output comes from the first group (a to d).
• If sel[2] is 1, the output comes from the second group (e to h).
• Within each group, sel[1] and sel[0] determine which specific input is selected.

This modular approach makes the design readable, scalable, and easy to debug.