In realising F(W,X,Y,Z) with an 8:1 MUX, what is connected to the select lines and why?

W, X, Y to the selects, since each data input then covers two minterms differing in Z

Z, Y, X to the selects, since Z is the MSB

All four variables to the selects

2070 Chaitra · 4 marks

F(W,X,Y,Z) using 8:1 MUX

Short answer

Use an 8:1 MUX with W,X,Y as selects. Data inputs: I0=Z, I1=Z', I2=Z, I3=Z, I4=Z', I5=Z', I6=1, I7=Z. One NOT gate provides Z'. The output implements the given minterms.

Realize the logic circuit of the following using 8:1 MUX. F(W,X,Y,Z) = Σm(1,2,5,7,8,10,12,13,15)

Use $W, X, Y$ as the select lines $S_2S_1S_0$ of the 8:1 MUX and connect $Z$ , $Z'$ , 0 or 1 to the data inputs. Input $I_j$ covers minterms $2j$ ( $Z = 0$ ) and $2j+1$ ( $Z = 1$ ).

Required minterms: 1, 2, 5, 7, 8, 10, 12, 13, 15.

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

             +--------+
  Z -------->| I0     |
  Z' ------->| I1     |
  Z -------->| I2     |
  Z -------->| I3 8:1 |----> F
  Z' ------->| I4 MUX |
  Z' ------->| I5     |
  1 -------->| I6     |
  Z -------->| I7     |
             +--------+
              W  X  Y
  (Z' from one NOT gate)

Check: $WXYZ = 1100$ (12): select 110 → $I_6 = 1$ , so $F = 1$ . $WXYZ = 1001$ (9): select 100 → $I_4 = Z' = 0$ , so $F = 0$ (9 is not a minterm). Correct.

✓ Answer checked by Claude Opus 5.5 (high effort)

Σ(0,2,3,6,7,8,12,13,15) using 8×1 MUX · Digital Logic, chapter 4
K-map Σ(0,1,4,8,10,11,12)+d, realize circuit · Digital Logic, chapter 3 · asked 2×
K-map ΠM(0,2,4,6,7,8,10,13,15) and 8:1 MUX · Digital Logic, chapter 3
K-map Σ(0,2,3,4,7,8,10,13)+d, logic circuit · Digital Logic, chapter 3
32:1 MUX tree; implement Σm(0,1,3,8,9,13,15) · Digital Logic, chapter 4
K-map Σm(7,9,12,13,14,15)+d, NOR-only · Digital Logic, chapter 3
Q and center frequency; realize −2000/(s²+500s+10⁶) · Filter Design, chapter 6
Tow-Thomas LPF derivation; realize −2000/(s²+500s+10⁶) · Filter Design, chapter 6
Hill road earthwork, chainage 12-15 · Estimating and Costing, chapter 6
Standard error; population 12,19,13,16 · Probability and Statistics, chapter 4

All Digital Logic chapter 4 questions →

F(W,X,Y,Z) using 8:1 MUX

Related questions