Common Function 9/19/2012 1 L06: Common Function Multiplexer Decoder NAND / NOR ROM (Read Only Memory)
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Common Function
9/19/2012 1L06: Common Function
Multiplexer
Decoder
NAND / NOR
ROM (Read Only Memory)
NAND / NOR
9/19/2012 2L06: Common Function
More Theorem (DeMorgan)
(A + B)’ = A’ * B’
NAND / NOR
More Theorem (DeMorgan)
(A + B)’ = A’ * B’
=
NAND / NOR
More Theorem (DeMorgan)
(A + B)’ = A’ * B’ (A * B)’ = A’ + B’
NAND / NOR
More Theorem (DeMorgan)
(A + B)’ = A’ * B’ (A * B)’ = A’ + B’
=
NAND / NOR
More Theorem (DeMorgan)
(A + B)’ = A’ * B’ (A * B)’ = A’ + B’
= =
NAND / NOR
More Theorem (DeMorgan)
(A + B)’ = A’ * B’ (A * B)’ = A’ + B’
NAND / NOR
A
AB + AC
B
A
C
NAND / NOR
A
AB + AC
B
A
C
A
AB + AC
B
A
C
?
=
NAND / NOR
More Theorem (DeMorgan)
(A + B)’ = A’ * B’ (A * B)’ = A’ + B’
A
AB + AC
B
A
C
A
AB + AC
B
A
C
Why NAND and NOR gates?
=
NAND / NOR
Common Function
9/19/2012 12L06: Common Function
Common Function
9/19/2012 13L06: Common Function
E
D
A
B
Cf
Common Function
9/19/2012 14L06: Common Function
E’
D
A
B
Cf
Common Function
9/19/2012 15L06: Common Function
E’
D
A
B
Cf
=
Common Function
9/19/2012 16L06: Common Function
D
A
B
CfE
Common Function
9/19/2012 17L06: Common Function
D
A
B
C’fE
Common Function
9/19/2012 18L06: Common Function
D
A
BfE
C’
Common Function
9/19/2012 19L06: Common Function
D
A
BfE
C’
Common Function
9/19/2012 20L06: Common Function
Common Function
9/19/2012 21L06: Common Function
i0
S
Zi1
0
2 to 1 Multiplexer
Common Function
9/19/2012 22L06: Common Function
i0
S
Z
1
i1
2 - 1 MUX
Common Function
9/19/2012 23L06: Common Function
4 - 1 MUX
S0
i0
Zi1
i2
i3
S1
Common Function
9/19/2012 24L06: Common Function
8 - 1 MUX
S1
i0
Z
i1
i2
i3
i4
i5
i6
i7
S0S2
Common Function
9/19/2012 25L06: Common Function
i0
S
Zi1
0
2 to 1 Multiplexer
Z = S’ * i0 + S * i1
Common Function
9/19/2012 26L06: Common Function
4 - 1 MUX
S0
i0
Zi1
i2
i3
S1
Z = S1’ * S0’ * i0 + S1’ * S0 * i1 +
S1 * S0’ * i2 + S1 * S0 * i3
Common Function
9/19/2012 27L06: Common Function
8 - 1 MUX
S1
i0
Z
i1
i2
i3
i4
i5
i6
i7
S0S2
Z = S2’ * S1’ * S0’ * i0 + S2’ * S1’ * S0 * i1 +
S2’ * S1 * S0’ * i2 + S2’ * S1 * S0 * i3 +
S2 * S1’ * S0’ * i4 + S2 * S1’ * S0 * i5 +
S2 * S1 * S0’ * i6 + S2 * S1 * S0 * i7
Common Function
9/19/2012 28L06: Common Function
Common Function
9/19/2012 29L06: Common Function
4 - 1 MUX
S0
i0
Zi1
i2
i3
S1
Common Function
9/19/2012 30L06: Common Function
4 - 1 MUX
S0
i0
Zi1
i2
i3
S1
Z = S’ * i0 + S * i1
Common Function
9/19/2012 31L06: Common Function
4 - 1 MUX
S0
i0
Zi1
i2
i3
S1
i0
S
Zi1
i0
S
Zi1
i0
S
Zi1
i0
i1
i2
i3
S0 S1
Z
Common Function
9/19/2012 32L06: Common Function
8 - 1 MUX
S1
i0
Z
i1
i2
i3
i4
i5
i6
i7
S0S2
Common Function
9/19/2012 33L06: Common Function
8 - 1 MUX
S1
i0
Z
i1
i2
i3
i4
i5
i6
i7
S0S2
Z = S2’ * S1’ * S0’ * i0 + S2’ * S1’ * S0 * i1 +
S2’ * S1 * S0’ * i2 + S2’ * S1 * S0 * i3 +
S2 * S1’ * S0’ * i4 + S2 * S1’ * S0 * i5 +
S2 * S1 * S0’ * i6 + S2 * S1 * S0 * i7
Common Function
9/19/2012 34L06: Common Function
8 - 1 MUX
S1
i0
Z
i1
i2
i3
i4
i5
i6
i7
S0S2
i0
S
Zi1 ZS0
i0
Zi1
i2
i3
S1
S0
i0
Zi1
i2
i3
S1
S1 S0 S2
i0
i1
i2
i3
i4
i5
i6
i7
Common Function
9/19/2012 35L06: Common Function
Common Function
9/19/2012 36L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1
Common Function
9/19/2012 37L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1Z
Ci
A
A
Ci
B
B
Common Function
9/19/2012 38L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1
Common Function
9/19/2012 39L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1 S0
i0
Z
i1
i2
i3
S1
Common Function
9/19/2012 40L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1 S0
i0
Z
i1
i2
i3
S1
A B
Common Function
9/19/2012 41L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1 S0
i0
Z
i1
i2
i3
S1
A B0 0
0
Common Function
9/19/2012 42L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1 S0
i0
Z
i1
i2
i3
S1
A B0 0
0
0 1
Ci
Common Function
9/19/2012 43L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1 S0
i0
Z
i1
i2
i3
S1
A B0 0
0
0 1
Ci
1 0
Ci
Common Function
9/19/2012 44L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1 S0
i0
Z
i1
i2
i3
S1
A B0 0
0
0 1
Ci
1 0
1
1 1
Ci
Common Function
9/19/2012 45L06: Common Function
A=1
B=1
Ci=1
0
0
0
1
0
1
1
1 S0
i0
Z
i1
i2
i3
S1
A B
0
Ci
1
Ci
Common Function
9/19/2012 46L06: Common Function
Common Function
9/19/2012 47L06: Common Function
a=1
b=1
c=1
0
0
1
1
0
1
0
1
d=1
0 0 00
0 0 11
Common Function
9/19/2012 48L06: Common Function
a=1
b=1
c=1
0
0
1
1
0
1
0
1
d=1
0 0 00
0 0 11
S0
i0
Z
i1
i2
i3
S1
Common Function
9/19/2012 49L06: Common Function
a=1
b=1
c=1
0
0
1
1
0
1
0
1
d=1
0 0 00
0 0 11
S0
i0
Z
i1
i2
i3
S1
A C
Common Function
9/19/2012 50L06: Common Function
a=1
b=1
c=1
0
0
1
1
0
1
0
1
d=1
0 0 00
0 0 11
S0
i0
Z
i1
i2
i3
S1
A C0 0
b
Common Function
9/19/2012 51L06: Common Function
a=1
b=1
c=1
0
0
1
1
0
1
0
1
d=1
0 0 00
0 0 11
S0
i0
Z
i1
i2
i3
S1
A C0 0
b
0 1
0
Common Function
9/19/2012 52L06: Common Function
a=1
b=1
c=1
0
0
1
1
0
1
0
1
d=1
0 0 00
0 0 11
S0
i0
Z
i1
i2
i3
S1
A C0 0
b
0 1
0
1 0
d
Common Function
9/19/2012 53L06: Common Function
a=1
b=1
c=1
0
0
1
1
0
1
0
1
d=1
0 0 00
0 0 11
S0
i0
Z
i1
i2
i3
S1
A C0 0
b
0 1
0
1 0
d
d’
1 1
Common Function
9/19/2012 54L06: Common Function
a=1
b=1
c=1
0
0
1
1
0
1
0
1
d=1
0 0 00
0 0 11
S0
i0
Z
i1
i2
i3
S1
A C
b
0
d
d’
Common Function
9/19/2012 55L06: Common Function
Common Function
9/19/2012 56L06: Common Function
a=1
b=1
c=1
0
0
0
1
0
1
0
1
d=1
0 0 00
0 1 11
Common Function
9/19/2012 57L06: Common Function
a=1
b=1
c=1
0
0
0
1
0
1
0
1
d=1
0 0 00
0 1 11
S0
i0
Z
i1
i2
i3
S1
Common Function
9/19/2012 58L06: Common Function
a=1
b=1
c=1
0
0
0
1
0
1
0
1
d=1
0 0 00
0 1 11S1
i0
Z
i1
i2
i3
i4
i5
i6
i7
S0S2
Common Function
9/19/2012 59L06: Common Function
Common Function
9/19/2012 60L06: Common Function
Address Decoder
Common Function
9/19/2012 61L06: Common Function
Address Decoder
oeba2 a1 a0 t0 t1 t2 t3 t4 t5 t6 t7
0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 1 0 0 0 0 0 0
0 0 1 0 0 0 1 0 0 0 0 0
0 0 1 1 0 0 0 1 0 0 0 0
0 1 0 0 0 0 0 0 1 0 0 0
0 1 0 1 0 0 0 0 0 1 0 0
0 1 1 0 0 0 0 0 0 0 1 0
0 1 1 1 0 0 0 0 0 0 0 1
1 X X X 0 0 0 0 0 0 0 0
Common Function
9/19/2012 62L06: Common Function
Address Decoder
Common Function
9/19/2012 63L06: Common Function
Multiplexer
Address Decoder
DeMultiplexer
2 to 1
4 to 1
8 to 1
1 to 2
2 to 4
3 to 8
4 to 16
1 to 2
1 to 4
1 to 8
Common Function
9/19/2012 64L06: Common Function
Common Function
9/19/2012 65L06: Common Function
9/19/2012 P66L06: Common Function
Switch Logic
9/19/2012 67L06: Common Function
9/19/2012 68L06: Common Function
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