1. Multiplexing and Demultiplexing

2. Multiplexing
There are several data inputs and one of them is routed to the output
Like selecting a television channel
In addition to data inputs, there must be select inputs
How many select pins are needed?
Depends on number of inputs
Multiplexer aka MUX

3. Truth table for 2-to-1 MUX
Select
Data
Out S0 A B 1

4. Algebra for 2-to-1 MUX Take expressions for 1’s found in truth table
SAB + SAB + SAB + SAB
This can be factored as follows
SA(B+B) + S(A+A)B
(B+B) = 1
Not B or B, doesn’t care about B
SA + SB

5. Gates for 2-to-1 MUX
S0A
S0B

6. 4-to-1 MUX: truth table
Select
Data
Out S1 S0 A B C D 1

7. 4-to-1 MUX: gate version

8. Addresses
Each data input is assigned to a specific state of the select input
E.g. low-low, low-high, high-low, high-high
The state can be interpreted as binary numbers
00, 01, 10, 11
Two select  Four addresses
And these numbers are thought of as the “addresses” of the input

9. 4-to-1 MUX: truth table (revisited)
Select
Data
Out S1 S0 D0 D1 D2 D3 1

10. Demultiplexing one input is routed to one of several outputs
Like mail may be sent to any number of recipients
In addition to data input, there must be select inputs
To select from 2N data outputs requires N select inputs
Demultiplexer aka DeMUX

11. 1-to-4 DeMux: Truth table
Select
Data
Output S1 S0 A O0 O1 O2 O3 1

12. 1-to-4 DeMUX: gate version

13. Decoder A variation on the previous circuit is to have no input data
the selected output will be high, the others low
This can be used to activate a control pin on the selected part of circuit

14. 1-to-4 Decode: Truth table
Select
Output S1 S0 O0 O1 O2 O3 1

15. 1-to-4 Decode: gates

16. Decoder plus registers = RAM
Memory Address Register (MAR) holds an address associated with memory
Memory Data Register (MDR) holds data for writing to memory
Memory is a sequence of registers and a decoder
Decoder output is connected to control pins (load in this example) of the RAM

17. Decoder plus registers = RAM
Load pins
MDR
Decoder
MAR

18. The logic of ROM
fuse
Address lines
Decoder
“Burned”
fuse

19. Logic of ROM (Cont.) Fuses connect output of decoder to output of ROM
Normal voltage and current does not burn (“blow”) the fuse
So when the selected decoder output is high, all ROM output lines to which it is connected are also high

20. Logic of ROM (Cont.)
Higher voltage and current will break the connections
They are applied selectively to break certain connections
The ROM output is not affected by the decoder output if the connection is broken
(Implementation may be different, but this is the basic logic)