### Basics: Number Specification

Sized Number Specification

Representation: [size]'[base][number]
• [size] is written only in decimal and specifies the number of bits.
• [base] could be 'd' or 'D' for decimal, 'h' or 'H' for hexadecimal, 'b' or 'B' for binary, and 'o' or 'O' for octal.
• [number] The number is specified as consecutive digits. Uppercase letters are legal for number specification (in case of hexadecimal numbers).
Ex: 4'b1111 : 4-bit binary number
32'd1 : 32-bit decimal number
8'o3 : 8-bit octal number

Unsized Number Specification

By default numbers that are specified without a [base] specification are decimal numbers. Numbers that are written without a [size] specification have a default number of bits that is simulator and/or machine specific (generally 32).

Ex: 123 : This is a decimal number
'hc3 : This is a hexadecimal number
Number of bits depends on simulator/machine, generally 32.

x or z values

x - Unknown value.
z - High impedance value
An x or z sets four bits for a number in the hexadecimal base, three bits for a number in the octal base, and one bit for a number in the binary base.

Note: If the most significant bit of a number is 0, x, or z, the number is automatically extended to fill the most significant bits, respectively, with 0, x, or z. This makes it easy to assign x or z to whole vector. If the most significant digit is 1, then it is also zero extended.

Negative Numbers

Representation: -[size]'[base][number]

Ex: -8'd9 : 8-bit negative number stored as 2's complement of 8
-8'sd3 : Used for performing signed integer math
4'd-2 : Illegal

Underscore(_) and question(?) mark

An underscore, "_" is allowed to use anywhere in a number except in the beginning. It is used only to improve readability of numbers and are ignored by Verilog. A question mark "?" is the alternative for z w.r.t. numbers
Ex: 8'b1100_1101 : Underscore improves readability
4'b1??1 : same as 4'b1zz1

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### Setup and Hold TIme

Every flip-flop has restrictive time regions around the active clock edge in which input should not change. We call them restrictive because any change in the input in this regions the output may be the expected one (*see below). It may be derived from either the old input, the new input, or even in between the two. Here we define, two very important terms in the digital clocking. Setup and Hold time.
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In the above figure, the shaded region is the restricted region. The shaded region is divided into two parts by the dashed line. The left hand side part of shaded region is the setup time period and the right hand side part is the hold time…

### Gate-Level Modeling

>> Introduction
>> Gate Primitives
>> Delays
>> Examples

Introduction

In Verilog HDL a module can be defined using various levels of abstraction. There are four levels of abstraction in verilog. They are:
Behavioral or algorithmic level: This is the highest level of abstraction. A module can be implemented in terms of the design algorithm. The designer no need to have any knowledge of hardware implementation.Data flow level: In this level the module is designed by specifying the data flow. Designer must how data flows between various registers of the design.Gate level: The module is implemented in terms of logic gates and interconnections between these gates. Designer should know the gate-level diagram of the design.Switch level: This is the lowest level of abstraction. The design is implemented using switches/transistors. Designer requires the knowledge of switch-level implementation details.
Gate-level modeling is virtually the lowest-level of abstraction, because t…