# 数字电路第一章习题(下)revised2

D ABC D C B A D C B A BCD A D C B A D C B A D C B A F ++++++=

()()()()

()()()()()

D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A F +++++++++++++++++++++++++++= 1-11

(1)()∑=7,6,5,4,2,01F (2)()∑=15,13,12,5,4,3,2,02F (3)()∑=5,4,2,1,03F

(4)()∑=15,14,7,6,5,4,24F (5)()∑=6,5,4,3,05F

(6)()∑=15,14,13,12,11,10,8,5,4,3,1,06F

(7)()∑=6,5,2,07F (8)()∑=14,11,7,5,4,18F 1-12

(1)()∏=7,01F

(2)()∏=15,13,7,6,5,3,22F (3)()∏=15,14,11,7,63F

(4)()∏=14,12,10,7,6,4,3,2,1,04F (5)()∏=7,5,4,35F

(6)()∏=13,11,10,9,8,5,1,06F

(7)()∏=7,5,3,27F

(8)()∏=15,12,9,7,4,2,08F

(a) ()∑=12,11,10,6,3,1F ()∏=15,14,13,9,8,7,5,4,2,0F (b) ()∑=15,13,9,8,6,4,3,0F

()∏=14,12,11,10,7,5,2,1F

1-14

(1)A AB BCD A B BCD A B ++=++=+ (2) 1AB BC A C A B C B +++=+++=

(3) ()()A B AB C D AB AB C D A B +++=++=+

(4)

AB AB AB A +===+(5)

BD BD BD BD +===(6) AB AB AB +==(7) ()()

()()C ABCD CD A B CD CD C AB CD CD AB CD CD C CD CD C D

+++++=++++=++=+

(8) 1AB BC C A AB AB BC C A A B A C B C +++=++++=+++= 1-15

（1）AB BC AC ++

A BC 010********

0011

1

1

1

AB BC AC A BC ++=+ （2）ABC BC AD CD +++

（3ABC ABCD ABCD A C AB A C BCD BCD +++=+++

（4）()()B C AD AC B D +++

AB

0001111000011110

00011110

01

1

1110

()()B C AD AC B D AB AC BD +++=++

（5）()

B C D ACD BCD BCD ?++

(B （6()ABC BCD AD A B CD ABD ABD AC ++++=++

（7）ABC CD AC BD ACD ++++

11111AB

0001111000011110

1111

1

1

11000

ABC CD AC BD ACD A C BC BC D ++++=+++

（8）()ACD ABCD AB C D D ++++

1(,,,)F A B C D AC ABD BCD ABC ACD =++++

（2）2(,,,)(2,3,6,8,913,15)F A B C D m =

?

1AB

0001111000011110

111

1

110

0000000

2(,,,)F A B C D ABC A CD ABD ABC =+++

（3）3(,,,)(0,2,4,6,8,10,13,15)F A B C D m =

3F （44(,,,)F A B C D AB CD BDC AD =+++

（5）5(,,,)(1,3,7,8,9,10,14)F A B C D M =

?

AB00011110

00 01 11 1011 111

1

1

11

000

5(,,,)

F A B C D AD BC ACD

=++

（6）

6(,,,)(3,4,7,8,11,12,15)

F A B C D M

=

6

F

（7

7(,,,)

F A B C D CD BC ACD

=++

（8）

8(,,,)(1,2,3,6,7,13,14,15)

F A B C D M

=?

AB00011110

00 01 11 101

11

111

1

1

8(,,,)

F A B C D CD AB ABC

=++

1-17

2(,,,)()()()()()

F A B C D A B C A B C B C D A C D A B D

=++++++++++

（3）

3(,,,)(1,2,3,7,8,9,12,14)

F A B C D m

=?

CD

AB00011110

00 01 11 10

11

1

1

11

11 00

00

00

3(,,,)()()()()()

F A B C D A C D A B D B C D A C D A B C

=++++++++++

（4）

4(,,,)(0,2,5,7,8,10,13,15)

F A B C D m

=

4

F

（5

5(,,,)()()()()

F A B C D C D A C D B C D A B D

=+++++++

（6）

6(,,,)(0,4,6,9,10,11,12,15)

F A B C D M

=?

CD

AB

0001111000011110

111111

110

00000

6(,,,)()()()()()()

F A B C D A C D B C D A B D A B D A B C A C D =++++++++++++（7）7(,,,)(2,3,4,10,11,13,14,15)F A B C D M =

7F （88(,,,)()()()()

()()()

F A B C D B C D A C D A B D A B C D A B C D A B C D A B C D =+++++++++=+++++++++

1-18

（1）1F ABCD ABCD ABCD =++ 约束条件 0AB AC +=

AB

0001111000011110

111

××××

××

000

1F BD =

（2）2F ABD ABD BCD =++ 约束条件 0AB AC +=

2F （33F BD AD BD =++

（4）4F ABCD BCD ABCD =++ 约束条件0BD BD +=

AB

00011110

00011110

1

11

1

××××

×

×

××

（5

0 5F （66F B CD =+

1-19

（1）1(,,,)(0,1,3,5,10,15)(2,4,9,11,14)F A B C D m d =

+

AB00011110

00 01 11 10111

1

1

1

××

××

×0

00

00

1(,,,)

F A B C D AB AC AC

=++

（2

2

F

（3

3(,,,)

F A B C D AD CD AB

=++

（4）

4(,,,)(1,3,7,11,13)(5,9,10,12,14,15)

F A B C D m d

=+

AB00011110

00 01 11 10

11

1

1

1

×

××××

×

0 0

00

4(,,,)

F A B C D D

=（5

5

F

（6

6(,,,)

F A B C D CD BC

=+

（7）

7(,,,)(3,5,6,7,10)(0,1,2,4,8,15)

F A B C D m d

=+

AB00011110

00 01 11 10

1

11

1

1××××

×

×

00

7(,,,)

F A B C D A BD

=+

（8

8

F