1. Figure 6.1. A 2-to-1 multiplexer.s s f w w f w 1 1 1 w 1
(a) Graphical symbol
(b) Truth table w w s f s w w 1 f 1
(c) Sum-of-products circuit
(d) Circuit with transmission gates
Figure A 2-to-1 multiplexer.

2. Figure 6.2. A 4-to-1 multiplexer.s s 1 s s f 1 w 00 w w 1 01 f 1 w 1 w 2 10 1 w w 2 3 11 1 1 w 3
(a) Graphic symbol
(b) Truth table s w s 1 w 1 f w 2 w 3
(c) Circuit
Figure A 4-to-1 multiplexer.

3. Figure 6.3. Using 2-to-1 multiplexers to build a 4-to-1 multiplexer.w w 1 1 f 1 w 2 w 3 1
Figure Using 2-to-1 multiplexers to build a 4-to-1 multiplexer.

4. Figure 6.4. A 16-to-1 multiplexer.s s 1 w w 3 w s 4 2 s 3 w 7 f w 8 w 11 w 12 w 15
Figure A 16-to-1 multiplexer.

5. Figure 6.5. A practical application of multiplexers.y 1 1 x y 2 2
(a) A 2x2 crossbar switch x 1 y 1 1 s x 2 y 2 1
(b) Implementation using multiplexers
Figure A practical application of multiplexers.

6. Please see “portrait orientation” PowerPoint file for Chapter 6
Figure Implementing programmable switches in an FPGA.

7. Figure 6.7. Synthesis of a logic function using multiplexers.w w w f 2 1 2 w 1 1 1 1 f 1 1 1 1 1
(a) Implementation using a 4-to-1 multiplexer w w f 1 2 w f 1 w 1 w 2 1 1 1 w w 2 2 1 1 f 1 1
(c) Circuit
(b) Modified truth table
Figure Synthesis of a logic function using multiplexers.

8. Figure 6.8. Three-input majority function.w w w f 1 2 3 w w f 1 2 1 w 1 3 1 w 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(a) Modified truth table w 2 w 1 w 3 f 1
(b) Circuit
Figure Three-input majority function.

9. w w w f 1 2 3 1 1 w Å w w 2 3 2 w 1 1 1 1 1 w 3 1 1 f 1 1 w Å w 2 3 1 1 1 1 1 1
(a) Truth table
(b) Circuit
Figure Three-input XOR function implemented with 2-to-1 multiplexers.

10. w w w f 1 2 3 w 3 w 1 1 2 w 1 1 1 w 3 w 1 1 3 1 1 f w 3 1 1 1 1 w 3 1 1 1 1
(a) Truth table
(b) Circuit
Figure Three-input XOR function implemented with a 4-to-1 multiplexer.

11. w w w f 1 2 3 w f 1 1 w w 2 3 1 1 w + w 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(b) Truth table w w 1 2 w 3 f
(b) Circuit
Figure Three-input majority function implemented using a 2-to-1 multiplexer.

12. Figure 6.12. Example circuits.

13. Figure 6.13. Example circuit.w w 2 1 w 3 f 1
Figure Example circuit.

14. Figure 6.14. Example circuits.w 1 f w w 1 2 f w 3 f w 1 w 4
(a) Using three 3-LUTs w 2 w 1 f f w w 2 3 w 4
(b) Using two 3-LUTs
Figure Example circuits.

15. Figure 6.15. An n-to-2n binary decoder.w y n
inputs 2 n w
outputs n – 1 y
Enable En 2 n – 1
Figure An n-to-2n binary decoder.

16. Figure 6.16. A 2-to-4 decoder. En w w y y y y w y 1 1 w y 1 1 1 y 1 11 2 3 w y 1 1 w y 1 1 1 1 1 y 1 1 1 2 y 1 1 1 1 En 3 x x
(a) Truth table
(b) Graphical symbol w y w 1 y 1 y 2 y 3 En
(c) Logic circuit
Figure A 2-to-4 decoder.

17. Figure 6.17. A 3-to-8 decoder using two 2-to-4 decoders.y y w w y y 1 1 1 1 y y 2 2 w 2 En y y 3 3 En w y y 4 w y y 1 1 5 y y 2 6 En y y 3 7
Figure A 3-to-8 decoder using two 2-to-4 decoders.

18. Figure 6.18. A 4-to-16 decoder built using a decoder tree.w w y y w w y y 1 1 1 1 y y 2 2 En y y 3 3 w y y 4 w y y 1 1 5 y y 2 6 w 2 w y En y y 3 7 w w y 3 1 1 y 2 En En y w y y 3 8 w y y 1 1 9 y y 2 10 En y y 3 11 w y y 12 w y y 1 1 13 y y 2 14 En y y 3 15
Figure A 4-to-16 decoder built using a decoder tree.

19. Figure 6.19. A 4-to-1 multiplexer built using a decoder.w w 1 s w y s w y f 1 1 1 y w 2 2 En y 1 3 w 3
Figure A 4-to-1 multiplexer built using a decoder.

20. w s w y w 1 s w y 1 1 1 y f 2 En y 1 3 w 2 w 3
Figure A 4-to-1 multiplexer built using a decoder and tri-state buffers.

21. Figure 6.21. A 2m x n read-only memory (ROM) block.
Sel
0/1
0/1
0/1
Sel 1
0/1
0/1
0/1 a
Sel 2
0/1
0/1
0/1
decoder a 1
Address m
-to-2 a m – 1 m
Sel 2 m – 1
0/1
0/1
0/1
Read
Data d d d n – 1 n – 2
Figure A 2m x n read-only memory (ROM) block.

22. Figure 6.22. A 2n-to-n binary encoder.w y n 2 n
inputs
outputs y w n – 1 2 n – 1
Figure A 2n-to-n binary encoder.

23. Figure 6.23. A 4-to-2 binary encoder.w w w w y y 3 2 1 1 1 1 1 1 1 1 1 1
(a) Truth table w w 1 y w 2 y w 1 3
(b) Circuit
Figure A 4-to-2 binary encoder.

24. Figure 6.24. Truth table for a 4-to-2 priority encoder.w w w w y y z 3 2 1 1 d d 1 1 1 x 1 1 1 x x 1 1 1 x x x 1 1 1
Figure Truth table for a 4-to-2 priority encoder.

25. Figure 6.25. A BCD-to-7-segment display code converter.w f b c w 1 d w g 2 e e c w 3 f g d
(a) Code converter
(b) 7-segment display w w w w a b c d e f g 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(c) Truth table
Figure A BCD-to-7-segment display code converter.

26. Figure 6.26. A four-bit comparator circuit.

27. module mux2to1 (w0, w1, s, f); input w0, w1, s; output f;
assign f = s ? w1 : w0;
endmodule 
Figure A 2-to-1 multiplexer specified using the conditional operator.

28. Figure 6.28. An alternative specification of a 2-to-1 multiplexer
module mux2to1 (w0, w1, s, f);
input w0, w1, s;
output f;
reg f;
or w1 or s)
f = s ? w1 : w0;
endmodule 
Figure An alternative specification of a 2-to-1 multiplexer
using the conditional operator.

29. module mux4to1 (w0, w1, w2, w3, S, f); input w0, w1, w2, w3;
input [1:0] S;
output f;
assign f = S[1] ? (S[0] ? w3 : w2) : (S[0] ? w1 : w0);
endmodule 
Figure A 4-to-1 multiplexer specified using the conditional operator.

30. module mux2to1 (w0, w1, s, f); input w0, w1, s; output f; reg f;
or w1 or s)
if (s==0)
f = w0;
else
f = w1;
endmodule
Figure Code for a 2-to-1 multiplexer using the if-else statement.

31. module mux4to1 (w0, w1, w2, w3, S, f); input w0, w1, w2, w3;
input [1:0] S;
output f;
reg f;
or w1 or w2 or w3 or S)
if (S == 2'b00)
f = w0;
else if (S == 2'b01)
f = w1;
else if (S == 2'b10)
f = w2;
else if (S == 2'b11)
f = w3;
endmodule
Figure Code for a 4-to-1 multiplexer using the if-else statement.

32. Figure 6.32. Alternative specification of a 4-to-1 multiplexer.
module mux4to1 (W, S, f);
input [0:3] W;
input [1:0] S;
output f;
reg f;
or S)
if (S == 0)
f = W[0];
else if (S == 1)
f = W[1];
else if (S == 2)
f = W[2];
else if (S == 3)
f = W[3];
endmodule
Figure Alternative specification of a 4-to-1 multiplexer.

33. Figure 6.33. Hierarchical code for a 16-to-1 multiplexer.
module mux16to1 (W, S16, f);
input [0:15] W;
input [3:0] S16;
output f;
wire [0:3] M;
mux4to1 Mux1 (W[0:3], S16[1:0], M[0]);
mux4to1 Mux2 (W[4:7], S16[1:0], M[1]);
mux4to1 Mux3 (W[8:11], S16[1:0], M[2]);
mux4to1 Mux4 (W[12:15], S16[1:0], M[3]);
mux4to1 Mux5 (M[0:3], S16[3:2], f);
endmodule 
Figure Hierarchical code for a 16-to-1 multiplexer.

34. Figure 6.34. A 4-to-1 multiplexer defined using the case statement.
module mux4to1 (W, S, f);
input [0:3] W;
input [1:0] S;
output f;
reg f;
or S)
case (S)
0: f = W[0];
1: f = W[1];
2: f = W[2];
3: f = W[3];
endcase
endmodule
Figure A 4-to-1 multiplexer defined using the case statement.

35. Figure 6.35. Verilog code for a 2-to-4 binary decoder.
module dec2to4 (W, Y, En);
input [1:0] W;
input En;
output [0:3] Y;
reg [0:3] Y;
or En)
case ({En, W})
3'b100: Y = 4'b1000;
3'b101: Y = 4'b0100;
3'b110: Y = 4'b0010;
3'b111: Y = 4'b0001;
default: Y = 4'b0000;
endcase
endmodule
Figure Verilog code for a 2-to-4 binary decoder.

36. Figure 6.36. Alternative code for a 2-to4 binary decoder.
module dec2to4 (W, Y, En);
input [1:0] W;
input En;
output [0:3] Y;
reg [0:3] Y;
or En)
begin
if (En == 0)
Y = 4'b0000;
else
case (W)
0: Y = 4'b1000;
1: Y = 4'b0100;
2: Y = 4'b0010;
3: Y = 4'b0001;
endcase
end
endmodule
Figure Alternative code for a 2-to4 binary decoder.

37. Figure 6.37. Verilog code for a 4-to-16 decoder.
module dec4to16 (W, Y, En);
input [3:0] W;
input En;
output [0:15] Y;
wire [0:3] M;
dec2to4 Dec1 (W[3:2], M[0:3], En);
dec2to4 Dec2 (W[1:0], Y[0:3], M[0]);
dec2to4 Dec3 (W[1:0], Y[4:7], M[1]);
dec2to4 Dec4 (W[1:0], Y[8:11], M[2]);
dec2to4 Dec5 (W[1:0], Y[12:15], M[3]);
endmodule
Figure Verilog code for a 4-to-16 decoder.

38. Figure 6.38. Code for a BCD-to-7-segment decoder.
module seg7 (bcd, leds);
input [3:0] bcd;
output [1:7] leds;
reg [1:7] leds;
case (bcd) //abcdefg
0: leds = 7'b ;
1: leds = 7'b ;
2: leds = 7'b ;
3: leds = 7'b ;
4: leds = 7'b ;
5: leds = 7'b ;
6: leds = 7'b ;
7: leds = 7'b ;
8: leds = 7'b ;
9: leds = 7'b ;
default: leds = 7'bx;
endcase
endmodule 
Figure Code for a BCD-to-7-segment decoder.

39. Table 6.1. The functionality of the 74381 ALU.

40. // ALU
module alu(s, A, B, F);
input [2:0] s;
input [3:0] A, B;
output [3:0] F;
reg [3:0] F;
or A or B)
case (s)
0: F = 4'b0000;
1: F = B - A;
2: F = A - B;
3: F = A + B;
4: F = A ^ B;
5: F = A | B;
6: F = A & B;
7: F = 4'b1111;
endcase
endmodule 
Figure Code that represents the functionality of the ALU chip.

41. Figure 6.40. Timing simulation for the 74381 ALU code.

42. Figure 6.41. Verilog code for a priority encoder.
module priority (W, Y, z);
input [3:0] W;
output [1:0] Y;
output z;
reg [1:0] Y;
reg z;
begin
z = 1;
casex(W)
4'b1xxx: Y = 3;
4'b01xx: Y = 2;
4'b001x: Y = 1;
4'b0001: Y = 0;
default: begin
z = 0;
Y = 2'bx;
end
endcase
endmodule
Figure Verilog code for a priority encoder.

43. Figure 6.42. A 2-to-4 binary decoder specified using the for loop.
module dec2to4 (W, Y, En);
input [1:0] W;
input En;
output [0:3] Y;
reg [0:3] Y;
integer k;
or En)
for (k = 0; k <= 3; k = k+1)
if ((W == k) && (En == 1))
Y[k] = 1;
else
Y[k] = 0;
endmodule
Figure A 2-to-4 binary decoder specified using the for loop.

44. Figure 6.43. A priority encoder specified using the for loop.
module priority (W, Y, z);
input [3:0] W;
output [1:0] Y;
output z;
reg [1:0] Y;
reg z;
integer k;
begin
Y = 2'bx;
z = 0;
for (k = 0; k < 4; k = k+1)
if(W[k])
Y = k;
z = 1;
end
endmodule
Figure A priority encoder specified using the for loop.

45. Please see “portrait orientation” PowerPoint file for Chapter 6
Table Verilog operators.

46. Figure 6.44. Truth tables for bitwise operators.
& 1 x j 1 x 1 x 1 1 x 1 1 1 1 x x x x x 1 x ^ 1 x ~^ 1 x 1 x 1 x 1 1 x 1 1 x x x x x x x x x
Figure Truth tables for bitwise operators.

47. Table 6.3. Precedence of Verilog operators.

48. Figure 6.45. Verilog code for a four-bit comparator.
module compare (A, B, AeqB, AgtB, AltB);
input [3:0] A, B;
output AeqB, AgtB, AltB;
reg AeqB, AgtB, AltB;
or B)
begin
AeqB = 0;
AgtB = 0;
AltB = 0;
if(A == B)
AeqB = 1;
else if (A > B)
AgtB = 1;
else
AltB = 1;
end
endmodule
Figure Verilog code for a four-bit comparator.

49. module addern (carryin, X, Y, S, carryout);
parameter n=32;
input carryin;
input [n-1:0] X, Y;
output [n-1:0] S;
output carryout;
wire [n:0] C;
genvar k;
assign C[0] = carryin;
assign carryout = C[n];
generate
for (k = 0; k < n; k = k+1)
begin: fulladd_stage
wire z1, z2, z3; //wires within full-adder
xor (S[k], X[k], Y[k], C[k]);
and (z1, X[k], Y[k]);
and (z2, X[k], C[k]);
and (z3, Y[k], C[k]);
or (C[k+1], z1, z2, z3);
end
endgenerate
endmodule
Figure Using the generate loop to define an n-bit ripple-carry adder.

50. Figure 6.47. Use of a task in Verilog code.
module mux16to1 (W, S16, f);
input [0:15] W;
input [3:0] S16;
output f;
reg f;
or S16)
case (S16[3:2])
0: mux4to1(W[0:3], S16[1:0], f);
1: mux4to1(W[4:7], S16[1:0], f);
2: mux4to1(W[8:11], S16[1:0], f);
3: mux4to1(W[12:15], S16[1:0], f);
endcase
// Task that specifies a 4-to-1 multiplexer
task mux4to1;
input [0:3] X;
input [1:0] S4;
output g;
reg g;
case (S4)
0: g = X[0];
1: g = X[1];
2: g = X[2];
3: g = X[3];
endtask
endmodule
Figure Use of a task in Verilog code.

51. Figure 6.48. The code from Figure 6.47 using a function.
module mux16to1 (W, S16, f);
input [0:15] W;
input [3:0] S16;
output f;
reg f;
// Function that specifies a 4-to-1 multiplexer
function mux4to1;
input [0:3] X;
input [1:0] S4;
case (S4)
0: mux4to1 = X[0];
1: mux4to1 = X[1];
2: mux4to1 = X[2];
3: mux4to1 = X[3];
endcase
endfunction
or S16)
case (S16[3:2])
0: f = mux4to1 (W[0:3], S16[1:0]);
1: f = mux4to1 (W[4:7], S16[1:0]);
2: f = mux4to1 (W[8:11], S16[1:0]);
3: f = mux4to1 (W[12:15], S16[1:0]);
endmodule
Figure The code from Figure 6.47 using a function.

52. Figure P6.1. The Actel Act 1 logic block.2 i 3 i 4 i 5 f i 6 i 7 i 8
Figure P6.1. The Actel Act 1 logic block.

53. Figure P6.2. Code for problem 6.18.
module
problem61_18 (W,
En,
y0,
y1,
y2,
y3) ;
input
[1:0]W;
input
En;
output
y0,
y1,
y2,
y3;
reg
y0,
y1,
y2,
y3;
always
@ (W or
En)
begin y0 = 0; y1 = 0; y2 = 0; y3 = 0; if
(En) if (W == 0) y0 = 1;
else if (W == 1) y1 = 1;
else if (W == 2) y2 = 1;
else y3 = 1;
end
endmodule
Figure P6.2. Code for problem 6.18.

54. Figure P6.3. Code for problem 6.22.
module
dec2to4(W, Y,
En);
input
[1:0]W;
input
En;
output
[0:3]Y;
reg
[0:3]Y;
integer k;
always
@(W or
En)
for (k = 0; k
<= 3; k =
k+1) if (W == k)
Y[k] =
En;
endmodule
Figure P6.3. Code for problem 6.22.

55. -to-4 decoder 2 Figure P6.4. A 4 x 4 ROM circuit. V a a d d d d DD 1 3
-to-4 decoder a 1 2 d d d d 3 2 1
Figure P6.4. A 4 x 4 ROM circuit.