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