Which variables are used as select lines for F(A,B,C,D)?

A, B, C as selects and D as data

D, C, B as selects and A as data

A, B as selects and C, D as data

How are the don't-cares 2, 6 and 13 used?

Each is taken as 0 or 1, whichever gives the simplest data input

They are ignored and the output is left floating

2082 Baisakh · 4 marks

Σm(0,1,3,4,8,9,15)+d using 8:1 MUX

Short answer

Connect A,B,C as selects. Set I0=I1=I4=1, I3=I5=I6=0, I2=D', I7=D. Don’t-cares at 2,6,13 are chosen to make inputs constant or simple functions of D, realizing F(A,B,C,D) = Σm(0,1,3,4,8,9,15)+d(2,6,13).

Implement the following function with 8:1 multiplexer F(A,B,C,D) = Σm(0,1,3,4,8,9,15) + dΣ(2,6,13).

Use $A, B, C$ as the select lines $S_2S_1S_0$ and $D$ (or $D'$ , 0, 1) on the data inputs. Input $I_j$ covers minterms $2j$ ( $D=0$ ) and $2j+1$ ( $D=1$ ).

Minterms: 0, 1, 3, 4, 8, 9, 15
Don't-cares: 2, 6, 13 (each can be taken as 0 or 1, whichever gives a simpler input)

Implementation table (X = don't care)

	$I_0$	$I_1$	$I_2$	$I_3$	$I_4$	$I_5$	$I_6$	$I_7$
$D'$	0	X(2)	4	X(6)	8	10	12	14
$D$	1	3	5	7	9	11	X(13)	15
Input	1	1	$D'$	0	1	0	0	$D$

Choices for the don't-cares:

$I_1$ : minterm 3 is 1; taking d(2) = 1 gives $I_1 = 1$ (no gate needed).
$I_3$ : minterm 7 is 0; taking d(6) = 0 gives $I_3 = 0$ .
$I_6$ : minterm 12 is 0; taking d(13) = 0 gives $I_6 = 0$ .

Circuit

             +--------+
  1 -------->| I0     |
  1 -------->| I1     |
  D --[NOT]->| I2     |
  0 -------->| I3 8:1 |----> F
  1 -------->| I4 MUX |
  0 -------->| I5     |
  0 -------->| I6     |
  D -------->| I7     |
             +--------+
              A  B  C

Check: $ABCD = 0100$ (4): select 010 → $I_2 = D' = 1$ , $F = 1$ . $ABCD = 0101$ (5): $I_2 = D' = 0$ , $F = 0$ . $ABCD = 1111$ (15): $I_7 = D = 1$ . All required minterms give 1 and all other non-don't-care minterms give 0.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Σm(0,1,3,4,8,9,15)+d using 8:1 MUX

Implementation table (X = don't care)

Circuit

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