dc2-4 decoder mux
DESCRIPTION
EEE 21TRANSCRIPT
Combinational Circuits
Decoder and ROM Multiplexer
PLA Oct. 22/23, 2015
Review of Combinational Blocks
• Encoder/Decoder • Multiplexer/Demultiplexer • ROM • PAL, PLA
Decoder and ROM
• Expansion: Using only 2x4 decoders with enable input, implement a 3x8 decoder.
• Logic Implementation: Using only 2x4 decoders and OR gates, implement the function
F(A, B, C) = ∑m(0, 3, 5, 6)
Multiplexer
• Mux Expansion: How do you implement a 16x1 Mux using only 4x1 Mux's?
• Logic Implementation: Using only 4x1 multiplexers, implement the function
F(A, B, C, D) = ∑m(0, 3, 5, 6, 8, 9, 14, 15)
16x1 Mux Using 4x1 Mux's
4×1 0 1 2 3 S1 S0
4×1 0 1 2 3 S1 S0
4×1 0 1 2 3 S1 S0
4×1 0 1 2 3 S1 S0
4×1 0 1 2 3 S1 S0
C D
C D
C D
C D
‘0’ ‘1’
A B
F
x0 x1 x2 x3
x4 x5 x6 x7
x8 x9 x10 x11
x12 x13 x14 x15
A B C D F
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 0
0 1 0 1 1
0 1 1 0 1
0 1 1 1 0
1 0 0 0 1
1 0 0 1 1
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 1
1 1 1 1 1
A = yz’ + xz’ + x’y’z
xy 00 01 11 10 z 0 0 1 1 1
1 1 0 0 0
B = A + xy xy 00 01 11 10 z 0 0 1 1 1
1 1 0 1 0
C = z + x’y xy 00 01 11 10 z 0 0 1 0 0
1 1 1 1 1
Product term
Inputs Outputs
x y z A A B C
1 yz’ - 1 0 - 1 - -
2 xz' 1 - 0 - 1 - -
3 x’y’z 0 0 1 - 1 - -
4 A - - - 1 - 1 -
5 xy 1 1 - - - 1 -
6 - - - - - - - -
7 z - - 1 - - - 1
8 x’y 0 1 - - - - 1
9 - - - - - - - -
PAL personality matrix Product term: - = all fuse blown Input side: 1 = asserted in term 0 = deasserted in term - = not used in term Output side: 1 = used in output - = not used in output
Seatwork
• Determine the simplified SOP expression for F1 and F2.
• Show the truth table for function F.
4×1 0 1 2 3 S1 S0
2×1 0 1 S0
2×1 0 1
S0
B C
B
A
F
0 1 1 0
1 C’
F1
F2