Medium-Scale Integrated Circuits

Using a 74LS151 (8-to-1 multiplexer) to Implement a Function of Four Variables

• Group row 0 with row 1; 2 with 3,…, and 14 with 15.
• Connect the three most significant variables W, X, and Y to select lines S2 (MS), S1, and S0 (preserve order of significance).
• For each pair of rows, compare the two function values to the Z column. Each input D0 to D7 must be one of 0, 1, Z, or Z′ as noted below.
• Enable the chip. The function output is the MUX output, Y-out.
• F′ is available if needed.

Row	W	X	Y	Z	F(W,X,Y,Z)	Input
0	0	0	0	0	0
1	0	0	0	1	0	D0 = 0
2	0	0	1	0	0
3	0	0	1	1	1	D1 = Z
4	0	1	0	0	1
5	0	1	0	1	0	D2 = Z’
6	0	1	1	0	1
7	0	1	1	1	1	D3 = 1
8	1	0	0	0	1
9	1	0	0	1	1	D4 = 1
10	1	0	1	0	1
11	1	0	1	1	0	D5 = Z’
12	1	1	0	0	0
13	1	1	0	1	1	D6 = Z
14	1	1	1	0	0
15	1	1	1	1	0	D7 = 0

74LS151

0 ¡	EN
Y	S0(LS)
X	S1
W	S2(MS)
0	D0	Y-out	F(W,X,Y,Z)
Z	D1	Y-out	¡ F’(W,X,Y,Z)
Z’	D2
1	D3
1	D4
Z’	D5
Z	D6
0	D7

Using a Decoder to Implement a Function

• Choose the version of the function with the fewest min or max terms.
• When enabled, the active-low decoder shown below generates max terms of the address variables A2, A1, and A0. For example, when A2, A1, and A0 = 1 0 0, M4 is generated at Y4_L. In this case, Y4_L = “0”; all other outputs are “1.”
• Use an external AND gate to combine max terms.
• Use an external NAND gate to combine min terms.

Decoder Example 1:

F(X, Y, Z) = PM(0, 2, 3, 5, 7) = Sm(1, 4, 6)

Enable the decoder. Connect input variables X (MS), Y, and Z to address lines A2, A1, and A0. NAND decoder outputs 1, 4, 6 (this effectively OR’s the min terms of the same number using DeMorgan’s Theorems.)

74LS138

		G1	Y0	¡	Y0_L
G2A_L	¡	G2A	Y1	¡	Y1_L
G2B_L	¡	G2B	Y2	¡	Y2_L
			Y3	¡	Y3_L
			Y4	¡	Y4_L
Z		A0 (LS)	Y5	¡	Y5_L
Y		A1	Y6	¡	Y6_L
X		A2 (MS)	Y7	¡	Y7_L

Decoder Example 2:

G(X, Y, Z) = PM(0, 3, 4)

Enable the decoder. Connect input variables X (MS), Y, and Z to address lines A2 (MS), A1, and A0. Use an AND gate to combine decoder outputs 0, 3, 4 (the max terms).