To implement a 4-variable function on an 8:1 MUX as in this answer, what drives the select lines and the data inputs?

A, B, C drive the select lines; the data inputs are 0, 1, D or D'

A, B, C, D all drive the select lines

D and C drive the select lines; the data inputs are A and B

A, B, C drive the data inputs; D drives all select lines

Why is I1 connected to logic 1 for F = Σ(0,2,3,5,8,12,14)?

Both minterms 2 and 3 are in F, so F=1 whatever D is

Neither minterm 2 nor 3 is in F

2078 Bhadra · 4+3 marks

Σ(0,2,3,5,8,12,14) using 8:1 MUX; add with full adders

Short answer

For the MUX, use A,B,C as selects; I0=D', I1=1, I2=D, I3=0, I4=D', I5=0, I6=D', I7=D'. One inverter gives D'. For binary addition, 1011 + 1101 = 11000 (carry 1, sum 1000) using four full adders.

Implement the given function F = Σ(0,2,3,5,8,12,14) using only one 8:1 MUX. Add the binary numbers 1011 and 1101 by using Full adders.

Implementing F = Σ(0,2,3,5,8,12,14) with one 8:1 MUX

Take $A, B, C$ as select lines ( $S_2S_1S_0$ ) and the LSB $D$ as the data variable. Each data input $I_i$ covers minterms $2i$ ( $D = 0$ ) and $2i+1$ ( $D = 1$ ).

$I_i$	ABC	Minterms ( $D$ =0, $D$ =1)	In F?	$I_i$
$I_0$	000	0, 1	yes, no	$D'$
$I_1$	001	2, 3	yes, yes	1
$I_2$	010	4, 5	no, yes	$D$
$I_3$	011	6, 7	no, no	0
$I_4$	100	8, 9	yes, no	$D'$
$I_5$	101	10, 11	no, no	0
$I_6$	110	12, 13	yes, no	$D'$
$I_7$	111	14, 15	yes, no	$D'$

D' --> I0 +--------+
1  --> I1 |        |
D  --> I2 |  8:1   |
0  --> I3 |  MUX   |--> F
D' --> I4 |        |
0  --> I5 |        |
D' --> I6 |        |
D' --> I7 +--------+
           S2 S1 S0
           A  B  C

Only one NOT gate is needed for $D'$ .

Adding 1011 and 1101 with full adders

Use a 4-bit parallel adder: four full adders FA0–FA3, with $C_0 = 0$ and each carry going to the next stage.

 A3B3     A2B2     A1B1     A0B0
  1 1      0 1      1 0      1 1
 [FA3]<-C3[FA2]<-C2[FA1]<-C1[FA0]<-C0=0
  |  \     |        |        |
 C4  S3    S2       S1       S0

Stage	$A_i$	$B_i$	$C_i$	$S_i$	$C_{i+1}$
FA0	1	1	0	0	1
FA1	1	0	1	0	1
FA2	0	1	1	0	1
FA3	1	1	1	1	1

Answer: $1011 + 1101 = 11000_2$ (carry $C_4 = 1$ , sum $S_3S_2S_1S_0 = 1000$ ). Check: $11 + 13 = 24 = 11000_2$ .

✓ Answer checked by Claude Opus 5.5 (high effort)

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Σ(0,2,3,5,8,12,14) using 8:1 MUX; add with full adders

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