Behavioral Modeling I

Behavioral modeling is the highest level of abstraction in the Verilog HDL. The other modeling techniques are relatively detailed. They require some knowledge of how hardware, or hardware signals work. The abstraction in this modeling is as simple as writing the logic in C language. This is a very powerful abstraction technique. All that designer needs is the algorithm of the design, which is the basic information for any design.

Most of the behavioral modeling is done using two important constructs: initial and always. All the other behavioral statements appear only inside these two structured procedure constructs.

The initial Construct

The statements which come under the initial construct constitute the initial block. The initial block is executed only once in the simulation, at time 0. If there is more than one initial block. Then all the initial blocks are executed concurrently. The initial construct is used as follows:

initial
begin
reset = 1'b0;
clk = 1'b1;
end

or

initial
clk = 1'b1;

In the first initial block there are more than one statements hence they are written between begin and end. If there is only one statement then there is no need to put begin and end.

The Always Construct

The statements which come under the always construct constitute the always block. The always block starts at time 0, and keeps on executing all the simulation time. It works like a infinite loop. It is generally used to model a functionality that is continuously repeated.

always
#5 clk = ~clk;

initial
clk = 1'b0;

The above code generates a clock signal clk, with a time period of 10 units. The initial blocks initiates the clk value to 0 at time 0. Then after every 5 units of time it toggled, hence we get a time period of 10 units. This is the way in general used to generate a clock signal for use in test benches.

always @(posedge clk, negedge reset)
begin
a = b + c;
    d = 1'b1;
end

In the above example, the always block will be executed whenever there is a positive edge in the clk signal, or there is negative edge in the reset signal. This type of always is generally used in implement a FSM, which has a reset signal.

always @(b,c,d)
begin
    a = ( b + c )*d;
    e = b | c;
end

In the above example, whenever there is a change in b, c, or d the always block will be executed. Here the list b, c, and d is called the sensitivity list.

In the Verilog 2000, we can replace always @(b,c,d) with always @(*), it is equivalent to include all input signals, used in the always block. This is very useful when always blocks is used for implementing the combination logic

Data flow modeling

Dataflow modeling is a higher level of abstraction. The designer no need have any knowledge of logic circuit. He should be aware of data flow of the design. The gate level modeling becomes very complex for a VLSI circuit. Hence dataflow modeling became a very important way of implementing the design.
In dataflow modeling most of the design is implemented using continuous assignments, which are used to drive a value onto a net. The continuous assignments are made using the keyword assign.

The assign statement

The assign statement is used to make continuous assignment in the dataflow modeling. The assign statement usage is given below:

assign out = vs0 + vs1; // vs0 + vs1 is evaluated and then assigned to out.

• The LHS of assign statement must always be a scalar or vector net or a concatenation. It cannot be a register.
• Continuous statements are always active statements.
• Registers or nets or function calls can come in the RHS of the assignment.
• The RHS expression is evaluated whenever one of its operands changes. Then the result is assigned to the LHS.
• Delays can be specified.

Examples:

assign vs[3:0] = vs0[3:0] & vs1[3:0];

assign {o3, o2, o1, o0} = vs0[3:0] | {vs1[2:0],vs2}; // Use of concatenation.

Implicit Net Declaration:

wire vs0, vs1;
assign out = vs0 ^ vs1;

In the above example out is undeclared, but verilog makes an implicit net declaration for out.

Implicit Continuous Assignment:

wire out = vs0 ^ vs1;

The above line is the implicit continuous assignment. It is same as,

wire out;
assign out = in0 ^ in1;

Delays

There are three types of delays associated with dataflow modeling. They are: Normal/regular assignment delay, implicit continuous assignment delay and net declaration delay.

Normal/regular assignment delay:

assign #10 out = in0 | in1;

If there is any change in the operands in the RHS, then RHS expression will be evaluated after 10 units of time. Lets say that at time t, if there is change in one of the operands in the above example, then the expression is calculated at t+10 units of time. The value of RHS operands present at time t+10 is used to evaluate the expression.

Implicit continuous assignment delay:

wire #10 out = vs0 ^ vs1;

is same as

wire out;
assign 10 out = vs0 ^ vs1;

Net declaration delay:

wire #10 out;
assign out = vs;

is same as

wire out;
assign #10 out = vs;

Gate level Modelling

The module is implemented in terms of logic gates and interconnections between these gates. Designer should know the gate-level diagram of the design

Gate primitives are predefined in Verilog, which are ready to use. They are instantiated like modules. There are two classes of gate primitives: Multiple input gate primitives and Single input gate primitives.
Multiple input gate primitives include and, nand, or, nor, xor, and xnor. These can have multiple inputs and a single output. They are instantiated as follows:

// Two input AND gate.
and and_1 (out, in0, in1);

// Three input AND gate.
and and_2 (out, in0, in1, in2);

// Two input OR gate.
or or_1 (out, in0, in1);

// Four input NOR gate.
or or_2 (out, in0, in1, in2, in3);

// Five input XOR gate.
xor xor_1 (out, in0, in1, in2, in3, in4);

// Two input XNOR gate.
xnor and_1 (out, in0, in1);

Single input gate primitives include not, buf, notif1, bufif1, notif0, and bufif0. These have a single input and one or more outputs. Gate primitives notif1, bufif1, notif0, and bufif0 have a control signal. The gates propagate if only control signal is asserted, else the output will be high impedance state (z). They are instantiated as follows:

// Inverting gate.
not not_1 (out, in);

// Two output buffer gate.
buf buf_1 (out0, out1, in);

// Single output Inverting gate with active-high control signal.
notif1 notif1_1 (out, in, ctrl);

// Double output buffer gate with active-high control signal.
bufif1 bufif1_1 (out0, out1, in, ctrl);

// Single output Inverting gate with active-low control signal.
notif0 notif0_1 (out, in, ctrl);

// Single output buffer gate with active-low control signal.
bufif0 bufif1_0 (out, in, ctrl);

Gate delays

Gate Delays

In Verilog, a designer can specify the gate delays in verilog code. This helps the designer to get a real time behavior of the logic circuit.

Rise delay: It is equal to the time taken by a gate output transition to 1, from another value 0, x, or z.

Fall delay: It is equal to the time taken by a gate output transition to 0, from another value 1, x, or z.

Turn-off delay: It is equal to the time taken by a gate output transition to high impedance state, from another value 1, x, or z.

• If the gate output changes to x, the minimum of the three delays is considered.
• If only one delay is specified, it is used for all delays.
• If two values are specified, they are considered as rise, and fall delays.
• If three values are specified, they are considered as rise, fall, and turn-off delays.
• The default value of all delays is zero.

and #(5) and_1 (out, in0, in1);
// All delay values are 5 time units.

and #(3,4,5) nand_1 (out, in0, in1);
// rise delay = 3, fall delay = 4, and turn-off delay = 5.

and #(3,4) or_1 (out, in0, in1);
// rise delay = 3, fall delay = 4, and turn-off delay = min(3,4) = 3.

There is another way of specifying delay times in verilog. Min:Typ:Max values for each delay. This helps designer to have a much better real time experience of design simulation, as in real time logic circuits the delays are not constant. The user can choose one of the delay values using +maxdelays, +typdelays, and +mindelays at run time. The typical value is the default value.

and #(4:5:6) and_1 (out, in0, in1);
// For all delay values: Min=4, Typ=5, Max=6.

and #(3:4:5,4:5:6,5:6:7) nand_1 (out, in0, in1);
// rise delay: Min=3, Typ=4, Max=5, fall delay: Min=4, Typ=5, Max=6, turn-off delay: Min=5, Typ=6, Max=7.

In the above example, if the designer chooses typical values, then rise delay = 4, fall delay = 5, turn-off delay = 6.

Basics : Data Types III

Vectors

Vectors can be a net or reg data types. They are declared as [high:low] or [low:high], but the left number is always the MSB of the vector.

wire [7:0] vs; // vs[7] is the MSB.
reg [0:15] vs_1; // vs_1[15] is the MSB.

In the above examples: If it is written as vs[5:2], it is the part of the entire vector which contains 4 bits in order: vs[5], vs[4], vs[3], vs[2].

Similarly vs_1[0:7], means the first half part of the vecotr vs_.1
Vector parts can also be specified in a different way:
vector_name[start_bit+:width] : part-select increments from start_bit in above example: vs_1[0:7] is same as vs_1[0+:8].

vector_name[start_bit-:width] : part-select decrements from start_bit in above example: vs[5:2] is same as vs[5-:4].

Arrays

Arrays of reg, integer, real, time, and vectors are allowed. Arrays are declared as follows:

reg vs1[0:7];
real vs3[15:0];
wire [0:3] vs4[7:0]; // Array of vector
integer vs5[0:3][6:0]; // Double dimensional array

Strings

Strings are register data types. For storing a character, we need a 8-bit register data type. So if you want to create string variable of length n. The string should be declared as register data type of length n*8.

reg [8*8-1:0] vs_1; // vs_1 is a string of length 8.

Time Data Types

Time data type is declared using the keyword time. These are generally used to store simulation time. In general it is 64-bit long.

time vs_1;
Vs_1 = $time; // assigns current simulation time to vs_1.

Basics : Data types II

Integers

Integer is a register data type of 32 bits. The only difference of declaring it as integer is that, it becomes a signed value. When you declare it as a 32 bit register (array) it is an unsigned value. It is declared using the keyword integer.

Real Number

Real number can be declared using the keyword real. They can be assigned values as follows:
real VS;

VS = 1.234; // Decimal notation.
VS = 3e4; // Scientific notation.

Parameter

Parameters are the constants that can be declared using the keyword parameter. Parameters are in general used for customization of a design. Parameters are declared as follows:

parameter vs = 123; // vs is a constant with value 123.

Keyword defparam can be used to change a parameter value at module instantiation. Keyword localparam is usedd to declare local parameters, this is used when their value should not be changed.

Basics : Data Types I

Value Set

The Verilog HDL value set consists of four basic values:

• 0 – represents a logic zero, or a false condition.
• 1 – represents a logic one, or a true condition.
• x – represents an unknown logic value.
• z – represents a high-impedance state.

The values 0 and 1 are logical complements of one another. Almost all of the data types in the Verilog HDL store all four basic values.

Nets

Nets are used to make connections between hardware elements. Nets simply reflect the value at one end(head) to the other end(tail). It means the value they carry is continuously driven by the output of a hardware element to which they are connected to. Nets are generally declared using the keyword wire. The default value of net (wire) is z. If a net has no driver, then its value is z.

Register

Registers are data storage elements. They hold the value until they are replaced by some other value. Register doesn’t need a driver, they can be changed at anytime in a simulation. Registers are generally declared with the keyword reg. Its default value is x. Register data types should not be confused with hardware registers, these are simply variables.

Synchronous Reset and Asynchronous Reset

A Reset is required to initialize a hardware design for system operation and to force an value into a known state for simulation.

A reset simply changes the state of the device to a user defined state. There are two types of reset, they are Synchronous reset and Asynchronous reset.

Synchronous Reset

A synchronous reset signal will only affect or reset the state of the flip-flop on the active/negative edge of the clock.

Advantages:

• The advantage to this type of topology is that the reset presented to all functional flip-flops is fully synchronous to the clock and will always meet the reset recovery time.
• Synchronous reset logic will synthesize to smaller flip-flops, particularly if the reset is gated with the logic generating the d-input. But in such a case, the combinational logic gate count grows, so the overall gate count savings may not be that significant.
• Synchronous resets provide some filtering for the reset signal such that it is not effected by glitches, unless they occur right at the clock edge. A synchronous reset is recommended for some types of designs where the reset is generated by a set of internal conditions. As the clock will filter the logic equation glitches between clock edges.

Disadvantages:

• The problem in this topology is with reset assertion. If the reset signal is not long enough to be captured at active clock edge (or the clock may be slow to capture the reset signal), it will result in failure of assertion. In such case the design needs a pulse stretcher to guarantee that a reset pulse is wide enough to be present during the active clock edge.
• Another problem with synchronous resets is that the logic synthesis cannot easily distinguish the reset signal from any other data signal. So proper care has to be taken with logic synthesis, else the reset signal may take the fastest path to the flip-flop input there by making worst case timing hard to meet.
• In some power saving designs the clocked is gated. In such designed only asynchronous reset will work.
• Faster designs that are demanding low data path timing, can not afford to have extra gates and additional net delays in the data path due to logic inserted to handle synchronous resets.

Asynchronous Reset

An asynchronous reset will affect or reset the state of the flip-flop asynchronously i.e. no matter what the clock signal is. This is considered as high priority signal and system reset happens as soon as the reset assertion is detected.

Advantages:

• High speeds can be achieved, as the data path is independent of reset signal.
• Another advantage favoring asynchronous resets is that the circuit can be reset with or without a clock present.
• As in synchronous reset, no work around is required for logic synthesis.

Disadvantages:

• The problem with this type of reset occurs at logic de-assertion rather than at assertion like in synchronous circuits. If the asynchronous reset is released (reset release or reset removal) at or near the active clock edge of a flip-flop, the output of the flip-flop could go metastable.
• Spurious resets can happen due to reset signal glitches.

CHISEL : Vec

A Vec in chisel represents a collections signal (same type). These are similar to the array data structures in other languages. Each element in Vec can be accessed by an index. A Vec will be created by calling a constructor with two parameters:

• The number of elements
• The type of the elements

The combinations vec must be wrap into a wire.
val vs = Wire(Vec(3 , UInt(4.W)))

Individual elements of the vecot can be accessed by index
vs(0) := 1.U
vs(1) := 2.U
vs(2) := 3.U

A vector wrapped into a Wire is multiplexer. We can also wrap the vec into register to define the array of registers as shown below
val regfile = Reg(Vec(32, UInt(32.W))
The elements of that register are accessed by index
val idx = 1.U(2.W)
val dout = regfile(idx)

We can freely mix bundles and vectors, as shown below

val vecBundle = Wire(Vec(8, new vlsiscape() ) ) —> vlsispace() was a bundle defined

CHISEL : Bundle

In Chisel provides two constructs to group related signals

• A Bundle to group signals of different type.
• A Vec represents the collection of signal of same type.

A chisel Bundle groups several signals. The entire bundle can be accessed or individual field can be accessed by their names. User or Designer can define a bundle(collections of signals) by definnig a class which extends Bundle and list the fields as vals within the constructor block

class vlsispace() extends Bundle {
val vlsi = UInt(32.W)
val space = Bool()
}

To access the bundle in following way
val vs = Wire(new vlsispace())
vs.vlsi := 124.U
vs.space := false.B

val a = vs.space

By using the dot we can access the field of the particular constructor, which is commonly used in object oriented programming. A Bundle is similar to struct in C , a record in VHDL or struct in system verilog. A bundle can be referred as a whole as follows

val channel = vs

A bundle may as well contain a vector:

class BundleVec extends Bundle {
val vs = UInt(8.U)
val vector = Vec(4 , UInt(4,W))
}

When we want a register of a bundle type that needs a reset value, we first wire of that bundle and define the values for the bundle elements and then passing the bundle to RegInit:

val initval = Wire( new vlsispcae())
initval.vlsi := 1.U
initval.space := true.B

val channelreg = RegInt(initval)

n bit binary adder or ripple carry adder

By using full adder, a single 1-bit binary adders can be constructed from basic logic gates as shown below

But what if we wanted to add together two n-bit numbers, then n number of 1-bit full adders need to be connected or “cascaded” together to produce a adder known as a Ripple Carry Adder.

Ripple carry adder is simply “n“ number of 1-bit full adders cascaded together with full adder representing a single weighted column in a long binary addition. It is called a ripple carry adder because the carry signals produce a “ripple” effect through the binary adder from LSB to MSB.

Let us consider a three bit full adders to “add” together two 3-bit numbers, the two outputs of the first full adder will provide the first place digit sum (S) of the addition plus a carry-out bit that acts as the carry-in digit of the next binary adder. The second binary adder in the chain also produces a summed output (the 2nd bit) plus another carry-out bit and we can keep adding more full adders to the combination to add larger numbers, linking the carry bit output from the first full binary adder to the next full adder, and so forth. An example of a 3-bit adder is given below.

Let us consider A =4 , B=3, sum of A and B will be 7. In binary addition

There will be a overflow ,If the sum was greater than or equal to 2ⁿ one of the disadvantage in this adder. Let us consider A =4 , B=4, Sum of A and B will be 8 which is equal to 2³ and we will have a overflow .

There two main disadvantages in ripple carry adder

• Propagation delay:
  if inputs A and B changes, the sum at its output will not be valid until any carry-input has “rippled” through every full adder in the chain because the MSB of the sum has to wait for any changes from the carry input of the LSB. Consequently, there will be a finite delay before the output of the adder responds to any change in its inputs resulting in a accumulated/propagation delay. This delay can be neglected for 4 to 8 bits but we cannot neglect the delay for higher bits like 32 bits and more.
• Over flow:
  Overflow occurs when the two n bit numbers add together whose sum is greater than or equal to 2ⁿ

To reduce the propagation delay of carry_in we can use Carry Look Ahead Binary Adder

CHISEL: Counter in Chisel

In digital systems counter is plays a main role. Counters are used to keep a track of events , time intervals and no of interrupts etc. . Counter can be programmed in many languages like verilog, c , c++ , java, python, chisel etc. In this post we will see how to program a counter in chisel language.

Design a counter which starts counting from 0 till 9 and reset to 0 once it counts till 9.

val cntSpace = RegInit (0.U (8.U))—> defines a 8 bit register which initialize to 0 upon reset signal
cntSpace := Mux( cntSpace ===9.U , 0.U, cntSpace + 1.U)

:= ——> update register
When the cntSpace reaches to 9, it will initialize to 0 otherwise the cntSpace will be incremented by one

scan cell, scan chain

Scan cell is one of the DFT technique , to test the sequential circuits in the Asic/Soc design. Normal D flip flop are converted to scan flip flop, if the tool meets the following criteria

• Clock of the flip flop must be controllable
• The set/reset of the flops must be inactive during the shift mode.

Once the all the flops in the design meet the above two rules the tool will convert the d flops to scan flops by adding a mux as shown in figure above. Then the tools will stitch the scan cells into a scan chain according to the design requirements.

When Scan Enable is 0 (SE=0), all the scan chains in the design will be disconnected and the flops are connected to comb. logic

When Scan Enable is 1 (SE=1) , combinational logic will be bypassed and all scan cells will be connected to form a scan chain

When SE=1 , patterns are loaded to the scan chains and the data from the comb logic are captured when SE=0

Untestable faults in DFT

Faults list in design are categorized into sub categories. Faults class are mainly divided into

• Testable(TE)–> Faults can be tested by some patterns.
• Untestable(UT)–> Faults foe which no pattern exits to detect the faults

Untestable Faults: Are the faults for which no pattern exit to either detect or possible detect them. These faults cannot cause any functional failures. And so the tools excludes them while calculating the test coverage. Types of Untestable faults are

• Unused (UU)
• Tied (TI)
• Blocked(BL)
• Redundant Faults (RE)

• Unused (UU)
  • Any floating pins not used in the design come under UU faults
  • The unused faults class includes all the faults on circuit unconnected to any observation point

• Tied (TI)
  • This faults includes faults on gates where the point of the faults is tied to a value identical to the fault stuck value

• Blocked (BL)
  • Due to tied logic in the design few faults are blocked and these are categories into Blocked faults. By adding the observable test point we can increase the coverage report.

• Redundant (RE)
  • The faults which are undetectable by the tool by any pattern , are classified as redundant faults

Implement the inverter using nand/NOR gate

Before implementing the logic, we will have a look at the truth table of the NAND gate and the inverter.

NAND GATE

A	B	O
0	0	1
0	1	1
1	0	1
1	1	0

NOT GATE

A	O
0	1
1	0

Fro the NAND gate truth table we can conclude the following
When both the inputs are zero(0) ==> output is 1 (same as inverter)
when both the inputs are one(1) ==> output is 0 (same as inverter)

Thus we can implement the not gate by connecting the both inputs together as shown below

There is another way of implementation of inverter using NAND gate , from truth table when input pin A is high (logic one) Nand gate behavious as INVERTER

Before implementing the logic, we will have a look at the truth table of the NOR gate and the inverter.

NOR GATE

A	B	O
0	0	1
0	1	0
1	0	0
1	1	0

NOT GATE

A	O
0	1
1	0

case I:
From the NOR truth table we can see that when
both the inputs are zero(0) ==> output is 1(same as inverter)
both the inputs are one (1) ==> output is 0 (same as inverter)

Case II :
second way of implementation of Inverter using Nor Gate.

Different ways of Digital design representation

A digital design can be represented at various levels from three different angles

• Behavioral
• Structural
• Physical

This can be represented by Y chart

Behavioral Representation

• Specifies how a particular should respond to a given set of inputs
• May be specified by
  -Boolean Equations
  -Tables of input and output values
  -Algorithms written in standard HLL like C/C++
  -Algoriths written in special HDL like verilog or VHDL or CHISEL

Example:

———————————–An Algorithm level of description of carry(Cy)———————————-
module carry (cy, a,b,c);
input a,b,c;
output cy;
assign cy = (a&b)|(a&c)|(b&c);
endmodule

——————————Boolean behavioral specification for carry (cy)————————————
primitive carry (cy,a b,c);
input a,b,c;
output cy;
table
// a b c : cy
   1 1 ? : 1 ;
   1 ? 1 : 1 ;
   ? 1 1 : 1 ;
   0 0 ? : 0 ;
   0 ? 0 : 0 ;
   ? 0 0 : 0 ;
endtable
endprimitive

Structural Representation

• Specifies how components are interconnected
• In general, the description is a list of modules and their interconnects
  – called Netlist
  – can be represented at various levels
• At Structural Level, levels of abstraction are:
  – The module (functional) level
  – The Gate level
  – The switch level
  – The circuit level

Example:
——————————————–Structural Representation—————————————–
module carry (cy , a, b, c);
input a, b, c;
output cy;
wire w1,w2,w3;
  and g1 (w1, a, b);
  and g2 (w2, a, c);
  and g3 (w3, b, c);
  or g4 (cy, w1,w2,w3);
endodule

Physical Representation

• The lowest level of physical specification
  – Photo-mask information required by various processing steps in the fabrication process.
• At the module level, the physical layout for the adder may be defined by a rectangle or polygon, and collection of ports

Example:
———————————————–Physical representation————————————————-
A possible (partial) physical description of 4 bit adder

module adder4 ;
input [3:0] a,b;
input c;
output [3:0] s;
output cy;
boundary [0 0 130 500];
port x[0] aluminum width = 1 origin = [0,35];
port y[0] aluminum width = 1 origin = [0,85];
port c polysilicon width = 2 origin = [70,0];
port s[0] aluminum width = 1 origin = [120,65];

add a0 orgin =[0 , 0];
add a1 orgin =[0 ,120];
endmodule

Simplistic view of ASIC DESIGN flow

Steps in design flow

• Behavioral Design
  • Specifies the functionality of the chip
• Data path Design
  • Generates the netlist for the register transfer level components
• Logic Design
  • Generate the netlist of Gates/Flip-Flops or Standard cells
• Physical Design
  • Generate the final layout
• Manufacturing the chip in Fabrication unit

Some more Intermediate steps are required during the Design flow.

• Simulation for Verification
  • It should be carried out at various levels, which includes: Logic level, Switch level, Circuit level
• Formal Verification
  • Logical equivalence check will be carried at various levels, to check core design was not disturbed.
  • LEC/Formal Verification on the design was done between
    -RTL and Synthesised Netlist
    -Synthesized Netlist and DFT inserted Netlist
    -MBIST Inserted Netlsit and Synthesized Netlist, etc
• Testability analysis and Pattern Generation
  • Required to test the manufactured Devices

chisel:Registers

In digital design, register are the basic elements which are used widely. Chisel provides a register , which is collection of D Flip Flops. The register is connected to a clock and the output of the register updates on every rising edge. When an initialization value is provided at the declaration of thr register, it uses a synchronous reset connected to reset signal. A register can be any chisel type that can be represented as a collection of bits.

Below line defines an 8 bit register, initialized with 0 at reset:
val reg = RegInit(0.U(8.W))

An input is connected to the register with the := update operator and the output of the register can be used just with the name in an expression

reg := d
val q = reg

A register can also be connected to its input at the definition:

val nextReg = RegNext(d)

A register can also be initialized during the definition:

val bothReg = RegNext(d, 0.U)

does knowlege on Location of MEMORIES was important during mbist implementation

MBIST( Memory Built In Self Test) is implemented to test memories in the design for different types of faults. MBIST contains the processor and wrapper which will be wrapped arround the memories.The MBIST processor controlls the wrapper and generates various control signals during the memory testing. A design may have multiple processors depending on the number of memories, memory size, power, frequency and memory placement.

Memories which are placed near by are grouped together and controlled by single processor. Thereofore, we need the memory placement info to group the memories under a controller and this info was given to the DFT team in the form of DEF and floorplan snapshot. This info will be given by PD/PNR team.

What happens if memories are not grouped properly?
If memories are not grouped properly according to their physical location i.e memories under same processors are sitting at different corners. This will lead to MBIST logic spreading, which impacts on MBIST timing during the STA due to long paths or increase in congestion due to lots of criss-cross while implementing the PNR and also increases the unneccesary power consumtption.

CHISEL:multiplexer

A multiplexer is a circuit which selects between the input signals depending on select signal. In basic form of multipexer (2:1 mux) selects between two signals. Below fig represents the 2:1 multiplexer , depending upon the sel signal y will represent the input signal a or b

A multiplexer can be designed using logic gates. As the multiplexer is used more frequently in digital desgin, chisel provides the function called MUX

val results = Mux(sel , a, b)

where a is selected when sel is true, otherwise b is selected, type of sel is a chisel Bool. The inputs a and b can be any chisel base type or aggregate (bundlers or vectors) as long as they are same type

A Bundle to group signals of different types. A Vec to represents an indexable collection of signals of the same type