CA-Midterm_1-Review

Midterm_1 Review

• 1. Floating point number
• 2. How C works?
  • 2.1. C Compilation Simplified Overview
  • 2.2. Pointer
  • 2.3. Array
    • 2.3.1. Further explanations:
    • 2.3.2. Point past end of array
• 3. C Memory Managemen
  • 3.1. Where are Variables Allocated?
• 4. RISC-V
• 5. Combinatorial Logic
• 6. Sequence Logic

OverAll

Course page

1. Floating point number

$$
\begin{align}
&S = (-1)^{\text{Sign}}\\
&E = \text{Exponent}_2-127_{10}\\
&Value = S\times M\times2^E
\end{align}
$$

Summary

Tips:
Abt denorms: Normalization and hidden 1 is to blame!
The exponent of denorms: $E := -126$

2. How C works?

2.1. C Compilation Simplified Overview

• Generally a two part process of compiling .c files to .o files, then linking the .o files into executables;
• Assembling is also done (but is hidden, i.e., done automatically, by default);

E.G

Something abt macro constant

PI: no type.

2.2. Pointer

Just remember to initialize it, or it can point to “garbage”.

2.3. Array

The difference between char string1[] = "abc" , char string2[3] = "abc" and char *string3 = "abc".

string1 ends with '\0', string3 is only readable

2.3.1. Further explanations:

• What do these below mean? Be really careful!

  int arr[] = [ 3,5,6,7,9] ; 
  int *p = arr;  
  int (*p1)[5] = &arr;  			// p is a pointer, including 5 int elements, refering to arr.
  int *p2[5];				// p2 is an array, including 5 int pointer.
  int (*p)(void);				// p is a pointer pointing to a function which accepts nothing.
  int (*func arr[5])(float x);      	// func_arr is an array, including 5 function pointers, and they all accept float.

• Be carefull abt pointer in function

  void inc_ptr(int *p) { p = p + 1; }	void inc_ptr(int **h){ *h = *h + 1; }
  int A[3] = {50, 60, 70};	int A[3] = {50, 60, 70};
  int *q = A;	int *q = A;
  inc_ptr( q);	inc_ptr(&q);
  printf( "q = %d\n",*q)	printf( "q = %d\n",*q)

1. q = 50
2. q = 60

2.3.2. Point past end of array

• Array size n; want to access from 0 to n-1, but test for exit by comparing to address one element past the last member of the array.

int ar[10]={},*p, *q, sum=0;
p = &ar[0]; q = &ar[10];
while (p!=q) /* sum = sum+*p; p = p+1*/ 
sum += *p++

• C defines that one element past end of array must be a valid address, i.e., not causing an error

3. C Memory Managemen

• Stack: automatically resize itself upon function invocations. (StackOverflow)
• Heap: this part is used for dynamic memory allocation. (malloc, free)
• Static Data: Global and static variables, allocated in compile time.
• Code: Contains code of the program, immutable. Also called text segment.

3.1. Where are Variables Allocated?

• If declared outside a function, allocated in static storage

• If declared inside function, allocated on the stack and freed when function returns

  • main() is treated like a function

• For the above two types, the memory management is automatic

  • Don’t need to deallocating when no longer using them
  • A variable does not exist anymore once a function ends!

4. RISC-V

Seek for more details: RISC-V Green_card

5. Combinatorial Logic

• Be careful:

  $$
  \begin{equation}
  \begin{gathered}
  A = A + A\overline{D}\\
  \text{DeMorgan’s Law: } \overline{AB} = \overline{A} + \overline{B}, \overline{A+B} = \overline{A}\ \overline{B}
  \end{gathered}
  \end{equation}
  $$

6. Sequence Logic

• Some terminology:
  • Clk-to-q: (t_prop) is the time for a signal to propagate through a flip-flop.
  • Propagation delay: (t_combinational) is the longest delay for any combinational logic (which by definition is surrounded by two flip-flop)
  • Setup time: (t_setup) is the time before the rising clock edge that the input to a flip-flop must be valid.
  • Hold time: The minimum time during which the input must be valid after the clock edge

Therefore, to be more SPECIFIC:

Clk-to-q: when there is a rising edge, output propagate this time.
Setup time & Hold time, during which the input should be stable.
Also note that:
Combinatorial logic also has delays.

(Setup time violation) In a SDS, a system the clock period (or cycle time) must be at least as large as

$$
\begin{equation}
\begin{gathered}
t_{\text{prop}}(t_{\text{clk-to-q}})+t_{\text{combinational}}+t_{\text{setup}}\leq \text{min clock period}\\
\text{Max frequency = 1/min clock period}
\end{gathered}
\end{equation}
$$

(Hold time violation) In a feedback SDS(circuits contain register to register propagation), the hold time must not exceed:

$$
\text{hold time}\leq t_{\text{prop}}(t_{\text{clk-to-q}})+t_{\text{combinational}}
$$

E.G

Example of Setup & Hold time

Solution:

Setup time: the critical path of “outer” combinational circuit.
Hold time: The shortest path including self register.
ATT: Evaluate each register separately

Example of Setup & Hold time