Demultiplexer

2-way Dmux

Dmux is short for demultiplexer and does the inverse of what mux or multiplexer does. Given an input, the dmux select its output between several paths based on an address.

input	sel	a	b
input	0	input	0
input	1	0	input

{-
    {a, b} = {input, 0} if sel == 0
             {0, input} if sel == 1
-}
dmux input[n] sel[1] -> { a[n], b[n] }

What's that { a[n], b[n] } output? It's our first time seeing a function that returns more than one output. In Mathematics, we usually think of a function as a machine that accepts one or multiple inputs and produces a single output. Single output also makes working with return values a lot easier. However, for our dmux function, we clearly need to return two values. What do we do? To contain multiple outputs, we use a record. In Sim, a record is a bunch of key-value pairs:

{ a = 0
, b = 1
, c = 0
}

where a, b, and c are keys and 0, 1, and 0 are the keys' values.

The great thing about the record is that we always know the names of our many output values, just like we do for our function inputs. Plus, a record is a single value, just like 0 and input!

If you have ideas on how to use records and how to implement dmux, go ahead and implement it.

Hints

If you get stuck, click on "See Hints".

See Hints

Fill in the blanks below:

dmux input[n] sel[1] -> { a[n], b[n] } =
    let
        a =
            ___________________
        b =
            ___________________
    in
    { a = a, b = b }

4-way Dmux

input	sel	a	b	c	d
input	00	input	0	0	0
input	01	0	input	0	0
input	10	0	0	input	0
input	11	0	0	0	input

{-
    {a, b, c, d} = {input, 0, 0, 0} if sel == 00
                   {0, input, 0, 0} if sel == 01
                   {0, 0, input, 0} if sel == 10
                   {0, 0, 0, input} if sel == 11
-}
dmux_4_way input[n] sel[2] -> { a[n], b[n], c[n], d[n] }

Hints

If you get stuck, click on "See Hints".

See Hints

Fill in the blanks below:

dmux_4_way input[n] sel[2] -> { a[n], b[n], c[n], d[n] } =
    let
        { a = a, b = b } =
            ___________________
        { a = c, b = d } =
            ___________________
    in
    { a = ___________________
    , b = ___________________
    , c = ___________________
    , d = ___________________
    }

8-way Dmux

input	sel	a	b	c	d	e	f	g	h
input	000	input	0	0	0	0	0	0	0
input	001	0	input	0	0	0	0	0	0
input	010	0	0	input	0	0	0	0	0
input	011	0	0	0	input	0	0	0	0
input	100	0	0	0	0	input	0	0	0
input	101	0	0	0	0	0	input	0	0
input	110	0	0	0	0	0	0	input	0
input	111	0	0	0	0	0	0	0	input

{-
    {a, b, c, d, e, f, g, h} =
        {input, 0, 0, 0, 0, 0, 0, 0} if sel == 000
        {0, input, 0, 0, 0, 0, 0, 0} if sel == 001
        ...
        {0, 0, 0, 0, 0, 0, 0, input} if sel == 111
-}
dmux_8_way input[n] sel[3] -> { a[n], b[n], c[n], d[n], e[n], f[n], g[n], h[n] }

Hints

If you get stuck, click on "See Hints".

See Hints

Fill in the blanks below:

dmux_8_way input[n] sel[3] ->
    { a[n], b[n], c[n], d[n], e[n], f[n], g[n], h[n] } =
    let
        { a = a, b = b, c = c, d = d } =
            ___________________
        { a = e, b = f, c = g, d = h } =
            ___________________
        sel_when_0 output[n] -> [n] =
            ___________________
        sel_when_1 output[n] -> [n] =
            ___________________
    in
    { a = ___________________
    , b = ___________________
    , c = ___________________
    , d = ___________________
    , e = ___________________
    , f = ___________________
    , g = ___________________
    , h = ___________________
    }

🎉 We just completed all the common logic circuits for our computer!