Multiplexers 1 The output is equal to one of several input signals to the circuit The multiplexer selects which input signal to use as an output signal based on the value represented by a few more input signals, called select signals EECS Computer Use: Fundamentals A multiplexer (or mux) is a general circuit that produces a single output signal

Multiplexers 2 S0S1S2F 000D0 001D1 010D2 011D3 100D4 101D5 110D6 111D7 The control lines S0, S1, S2 determine which of eight other input lines (D0 – D7) are provided to the output “F” For example, if S0 S1 S2 = 000, the output will be equal to D0 In general, the binary values on n input control lines are used to determine which of 2 n other data lines are selected for output. EECS Computer Use: Fundamentals

Sequential Circuits 3 In this circuit, the output of the circuit also serves as input to the circuit. That is the existing state of the circuit is used to determine the next state of the circuit Digital circuits that store information form a sequential circuit. EECS Computer Use: Fundamentals

Circuit as Memory (S-R Latch) 4 Here we use 2 NAND gates An S-R latch stores a single binary digit (1 or 0) S = Set; R = Reset (or the control line) An example of one type of memory circuits is the S-R latch EECS Computer Use: Fundamentals

Circuit as Memory (S-R Latch) 5 The design of this circuit guarantees that the two outputs X and Y are always complements of each other The value of X at any point in time is considered to be the current state of the circuit: If X is 1, the circuit is storing a 1 If X is 0, the circuit is storing a 0 X = Y’ An S-R latch stores a single binary digit (1 or 0) EECS Computer Use: Fundamentals

Circuit as Memory (S-R Latch) 6 then if S = R = 1, X remains 1 and Y remains X = Y’ Suppose the current state of the circuit is 1 (i.e. X = 1), EECS Computer Use: Fundamentals

Circuit as Memory (S-R Latch) This means if both input values S and R are 1, then the circuit keeps its current state X = Y’ Suppose the current state of the circuit is 0 (i.e. X = 0), then if S = R = 1, X remains 0 and Y remains 1 EECS Computer Use: Fundamentals

Circuit as Memory (S-R Latch) 8 Go back to the case when the current state is 1 Now we purposely set S = 0 then X remains 1 and Y remains X = Y’ EECS Computer Use: Fundamentals But how does the output state (i.e. X) change?

Circuit as Memory (S-R Latch) X = Y’ No changes to X and Y EECS Computer Use: Fundamentals Now change S back to 1

Circuit as Memory (S-R Latch) X = Y’ 0 1 That means the output state can be changed from 1 to 0 by resetting R to 0 EECS Computer Use: Fundamentals Now change R to 0 Then the output of the bottom NAND will always give us 1, so Y = 1 and X = 0

Circuit as Memory (S-R Latch) X = Y’ Then Y remains at 1 and X remains at 0 Again, as long as S = R = 1, X remains at 0 and Y remains at 1 EECS Computer Use: Fundamentals Now change R to 1

Circuit as Memory (S-R Latch) X = Y’ Let’s try to change R to 0 Then Y remains at 1 and X remains at 0 So X remains at 0 and the state doesn’t change 0 1 EECS Computer Use: Fundamentals So how do we change X back to 1 (i.e. the previous state)?

Circuit as Memory (S-R Latch) X = Y’ By changing S, the output state goes back to 1 EECS Computer Use: Fundamentals So let’s go back and change S to 0 instead

Circuit as Memory (S-R Latch) 14 X = Y’ SRX (output state) 00Restricted combination 01X goes to 1 10X goes to 0 11No change Timing diagram: EECS Computer Use: Fundamentals So the truth table of the S-R latch is:

Integrated Circuits (Chip or IC) 15 An integrated circuit (IC) is a piece of silicon on which multiple gates are embedded IC are classified by the number of gates contained in them. EECS Computer Use: Fundamentals

Integrated Circuits (Chip or IC) 16 For example: An SSI chip has 14 pins: 8 for inputs to gates; 4 for output of the gates; 1 for ground; 1 for power. EECS Computer Use: Fundamentals

Integrated Circuits (Chip or IC) 17 So how can an IC has more than 100,000 gates on it? If we need 2 pins for input and 1 pin for output, that would need 300,000 pins! Key is that the gates are not independent, that is, many gates are combines to create complex circuits that require only a few input and output values. EECS Computer Use: Fundamentals

CPU Chips 18 Most important IC in any computer is the central processing unit (CPU) Each CPU chip contains a large number of pins – provides communication from the CPU to memory and I/O devices, and vice versa. EECS Computer Use: Fundamentals