F(w,x,y,z) = w’y’z + xz’ + wxy - Stevens Institute of...
11
Click here to load reader
Transcript of F(w,x,y,z) = w’y’z + xz’ + wxy - Stevens Institute of...
Homework 3 – due 6/2 3-5) Simplify the following Boolean functions, using four-variable maps:
(a) F(w,x,y,z) = Σ(1, 4, 5, 6, 12, 14, 15) (b) F(A,B,C,D) = Σ(0,1,2,4,5,7,11,15) (c) F(w,x,y,z) = Σ(2,3,10,11,12,13,14,15) (d) F(A,B,C,D) = Σ(0,2,4,5,6,7,8,10,13,15)
a) b)
1 1
0 1
0 1
0 0
0 0
1 0
0 0
1 1
00 01 11 10
01
00
10
11
wx\yz
F(w,x,y,z) = w’y’z + xz’ + wxy
1 1
1 1
1 0
0 1
0 0
0 0
1 0
1 0
00 01 11 10
01
00
10
11
AB\CD
F(A,B,C,D) = A’C’ + A’B’D’ + BCD + ACD
c) d)
1 1
1 0
1 1
0 1
1 0
0 1
0 1
1 0
00 01 11 10
01
00
10
11
AB\CD
F(A,B,C,D) = B’D’ + A’B + BD
0 0
0 0
0 0
1 1
0 0
1 1
1 1
1 1
00 01 11 10
01
00
10
11
Wx\yz
F(w,x,y,z) = x’y + wx
3-7) Simplify the following Boolean expressions, using four-variable maps:
(a) w’z + xz + x’y + wx’z (b) B’D + A’BC’ + AB’C + ABC’ (c) AB’C + B’C’D’ + BCD + ACD’ + A’B’C + A’BC’D (d) wxy + yz + xy’z’ + x’y
a)
b)
0 1
0 1
1 0
1 1
0 1
0 1
1 1
1 0
00 01 11 10
01
00
10
11
Wx\yz
F(w,x,y,z) = w’z + xz + x’y + wx’z = z + x’y
1 1
0 1
0 0
1 0
0 1
1 1
1 1
0 0
00 01 11 10
01
00
10
11
AB/CD
F(A,B,C,D) = B’D + A’BC’ + AB’C + ABC’ = B’D + BC’ + AB’C
c)
d)
0 1
1 0
1 0
1 1
1 0
0 0
1 1
1 1
00 01 11 10
01
00
10
11
AB/CD
F(A,B,C,D) = AB’C + B’C’D’ + BCD + ACD’ + A’B’C + A’BC’D = CD + B’D’ + AC + A’BD
F(w,x,y,z) = wxy + yz + xy’z + x’y = xz + wy + x’y
0 1
00 01
01
0 0 00
yz
wx
1 0
1 1
11 10
0 0
0 1
1 1
1 1 11
10
3-18) Draw a logic diagram using only two-input NAND gates to implement the following expression: (AB + A’B’)(CD’ + C’D)
(AB + A’B’)(CD’ + C’D)
A B
A’ B’
C D’
C’ D
A B
A’ B’
C D’
C’ D
BCD to 7-segment decoder for segments a-f: a- b- c- d- e- f-
a:
Calculator Clock,
or Counter Circuit
7 segment
BCDdata
0
5
1
6
2
7
3
8
4
9
a
b
c
d
e
f
g
w=8
x=4
y=2
z=1
1 1
1 0
0 1
0 0
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fa(w,x,y,z) = y’z’ + xz’ + xy’ + w
1 1
1 0
0 1
0 0
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fa’(w,x,y,z) = w’x’y + w’x’z + yz
b:
0 1
1 0
1 1
1 1
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fb(w,x,y,z) = y + w + xz + x’z’
0 1
1 0
1 1
1 1
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fb’(w,x,y,z) = w’x’y’z + w’xy’z’
c:
1 0
1 1
1 0
1 1
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fc(w,x,y,z) = x’ + w + y’z’ +yz
1 0
1 1
1 0
1 1
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fc’(w,x,y,z) = xy’z + xyz’
d:
1 1
1 1
1 1
1 0
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fd(w,x,y,z) = x + y’ + z
1 1
1 1
1 1
1 0
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fd’(w,x,y,z) = x’yz’
e:
0 1
1 0
0 1
1 1
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fe(w,x,y,z) = w + x’y + yz’ + x’y’z’ + xy’z
0 1
1 0
0 1
1 1
1 1
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Fe’(w,x,y,z) = xy’z’ + w’x’y’z + xyz
f:
0 0
1 0
0 1
0 1
1 0
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Ff(w,x,y,z) = x’z’ + yz’
0 0
1 0
0 1
0 1
1 0
X X
X X
X X
00 01 11 10
01
00
10
11
wx\yz
Ff’(w,x,y,z) = xy’ + z
![XZ axis Steel Extended Contact Slide Stages Stage size TSD ...€¦ · Axes of Travel XZ axis Micrometer Position Center Side Center Side Travel [mm] X axis ±3 Z axis ±3 X axis](https://static.fdocument.org/doc/165x107/60a33233301dac586036b9a6/xz-axis-steel-extended-contact-slide-stages-stage-size-tsd-axes-of-travel-xz.jpg)
![Powersoft - Octubre 2020 - SeeSound · 2020. 10. 14. · > ] W ] } K µ î ì î ì DK >K ^ Z/W /ME WsW y ^ ] y ^ ] u o ] ( ] } y ð> ^W = Ed } v ] îh l } v } v ^W X ð Æ ð ô](https://static.fdocument.org/doc/165x107/60b7effd469bf141401a4f35/powersoft-octubre-2020-seesound-2020-10-14-w-k-.jpg)
