# Which Is Legal Negative Number Representation in Verilog

-10`d5 Number 10 bits stored in addition two out of 5. I read about the representation of signed numbers and the book says that different representations express (almost) the same thing, but work better (or worse) under different circumstances: hexadecimal is suitable for a memory address, while scientific notation expresses large and lowercase numbers just as compactly. In this first article, we`ll explore how integers are represented and discuss the challenges of signed numbers in Verilog. Four types of state data Logical, reg, and wire data types can have one of four values: 0, 1, X, Z, where X is unknown and Z is a high impedance. For the purposes of this introduction in numbers, we will ignore X and Z. Is there a reason why a number declared as 6 bits is stored as 8 bits? In Verilog, size numbers may or may not be assigned. If the size is not declared, 32-bit is used by default. In addition, you need to select the number base and the options are decimal, hexadecimal, octal, and binary. If the base is not specified, the decimal base is used by default. You have to remember that -8d69 is just a bit of a model. reg is a type that contains bit patterns. This is the type of variable that teaches/performs unsigned arithmetic.

If your app requires negative values, you must handle signed numbers. The standard approach is to complete two, as with most software development. Verilog has undergone some revisions over the years and from 1995 to 2001, further additions were made, which are presented below. Negative numbers can be specified by placing a minus sign before the size of a constant number, making them signed numbers. Verilog internally represents negative numbers in complement format of 2. An optional sign identifier can be added for signed arithmetic. With the complement of two, addition, subtraction, and multiplication all work as with positive binary numbers. But what is the complement of the two? Complementary representations of both positives and negatives of an N-bit number give 2N. We know better that numbers are represented as decimals. Numbers can also be represented binary, octal, and hexadecimal.

By default, Verilog simulators treat numbers as decimals. In order to display them in a different radius, certain rules must be respected. Any number without a negative sign is a positive number. Or the indirect way would be “Unsigned”. It is not really a signed number, but an expression consisting of a unary negation applied to a positive constant. If the expression was -8`d130, the result would overflow. Sign constants are declared as 8`sd69 or just 69. KBK If you omit the base, the literal will be signed! This is not a problem most of the time, but it can lead to subtle mistakes.

We will discuss signed numbers in the next section. However, this is not the only possible representation: some systems use binary encoded decimal numbers (BCDs). Packed1 BCD uses a Nibble value (4 bits) to represent each decimal place. Imagine creating a game engine where the number of sprites is configurable: as a hardware designer, you face similar choices and trade-offs. How many bits do I need? Do I need signed numbers? Will BCD simplify my design? Is the fixed point accurate enough? In particular, note that if one or more operands are not signed, they will be treated as an unsigned comparison, which is different from what you expect from C. The usual way to change the sign of a number to two complements is to reverse the bits and add one: we are so familiar with different representations of numbers that we hardly think about it. The following sample file shows how Verilog handles signed and unsigned numbers. Size numbers are represented as shown below, with the size written only to indicate the number of bits in the number. Verilog supports both types of numbers, but with some limitations.

As in the C language, we do not have int and unint types to tell whether a number is signed or unsigned. Verilog gives you several options for displaying literal numbers. You can use binary, decimal, octal, or hexadecimal literals and specify their width in bits. Negative numbers are stored as a second compliment and the minus sign must be included before specifying the size. 122 – Unsized number without base, so it is a large number of 32 bits with a decimal value of 122. The most significant bit of a signed vector is always 1 for a negative number, so it is easy to determine if a value is negative: we get the main advantage of a sign bit without the drawbacks. The BCD representation requires eight bits to represent 42, two more than the old simple binary version. However, there are advantages, including easy display (every snack is a character) and the ability to accurately represent decimal numbers (such as 10.1). Unspecified numbers base_format are decimal places by default. Unspecified numbers have a default number of bits, depending on the type of simulator and machine. To get the compressed BCD representation, convert each decimal place to a 4-bit binary value: Verilog HDL allows you to specify integers like Welcome to my new series on math and algorithms with FPGA.

No matter what hardware you`re designing, you`re probably working with numbers. This series starts with the basics of Verilog numbers and covers simple mathematics, including division and CORDIC, before looking at more complex algorithms such as data compression. This article was last updated in August 2022. Caps are allowed to specify numbers if the base format is hexadecimal. You can specify constant numbers in decimal, hexadecimal, octal, or binary format. Negative numbers are represented as a complement to 2. When used in a number, the question mark (?) is the Verilog alternative to the z-sign. The underscore (_) is allowed anywhere in a number, except as the first character where it is ignored. Lexical conventions in Verilog are similar to C in that it contains a stream of tokens. A lexical token can consist of one or more characters, and tokens can be comments, keywords, numbers, strings, or spaces. All lines must end with a semicolon. We have talked a lot about the representation of numbers, but we have not done any calculations.

Negative numbers are specified by placing a minus sign in front of the size of a number. It is illegal to have a minus sign between base_format and the number. You rarely have to determine for yourself whether to add both; Verilog can do this for you. Net declarations can be wire, sort, supply0 and supply1. If you specify a maximum value, you must add a value to the value passed to \$clog 2: Multiplication is more complex, but FPGAs can handle it with dedicated DSP blocks. We`ll cover multiplication in the next part of this series: Multiplication by FPGA DSPs. Note: X is unknown and Z is high impedance, 1 is logical is high, or 1 and 0 are logically low or 0. This issue is often hidden because it does not occur if your setting is not a power of 2. For example, if you specify “240” as the MAX_VOLTAGE, no problems are displayed.

Later, increase MAX_VOLTAGE to “256”, and the design has a subtle flaw. Identifiers are variable names so that they can be referenced later. They consist of alphanumeric characters [a-z][A-Z][0-9], underlined _ or dollar signs \$, and are case sensitive. You can`t start with a dollar number or sign. The question I have now is, if I were to perform an operation on it, say myReg/2 So if you assign -8`D69 myReg, an implicit conversion to 187 will be done. Then myReg/2 = 187/2 = 93, unsigned. It is important to understand when and how SystemVerilog performs implicit type conversions in expressions and assignments. Forty-two require at least six binary digits to represent in this way. I know Verilog stores it as add-in 2, so it should be saved as. However, single-line comments can be nested within a multiline comment. However, spaces (spaces) and tabs (of the TAB key) are not ignored in strings.

In the following example, the string variable addr is set to “Earth” because spaces are preserved in strings. Would it be rated at -34? Or should we 10111011 and turn it into 187, then run the division and turn 93? For example, with values of four bits: 7 is 0111 and -7 is 1001 because 0111 + 1001 = 10000 (24). >> x Moves x digits to the right, >>> x moves to the right x digits, but the sign expands for signed types. It`s a good idea to specify the width and base for each literal, but they are optional. The best place to check this is the Language Reference Manual. As expected, this is a bit chaotic given Verilog`s “eh” parameter for correct input. 3`B010 – 3 bits wide with the value 010 in base two or 2 in decimal base. If we hard-code the width, the design will be damaged by changing the number of sprites. A more general definition is: type [msb_index:lsb_index] name; msb_index is the largest and lowest bit index lsb_index. I would add that 1. The bit and reg data types are not signed by default. 2.

The int, integer, longint, shortint and byte data types are signed by default. 3. All of these data types can use a signed or unsigned qualifier to change the default. myReg is not signed, so the print result is also unsigned*. If the result is to be signed, all operands must be signed. There are several ways to do this: So far, we`ve talked about endianness at the bit level, but this happens most often in the context of bytes.