Numbers

4-Value Logic Values

A scalar logic net can be one of four possible values:

Verilog logic values.

Value	Description
0	Zero, low, or false.
1	One, high, or true.
x	Unknown or uninitialized.
z	Undriven (floating).

Integers

Simple integers are numbers constructed from digits and possibly underscores. Underscores are ignored in numbers, so 42_839 is equivalent to 42839.

Examples:

124

+124

-124

42_839

Simple integers are signed unsized numbers. A simple integer specification may not contain an x or z.

Except in Verilog-A, integer numbers can be explicitly expressed in decimal, hexadecimal, octal, or binary notation. To do so, use s’bn; where s is an optional decimal number that indicates the size of the constant in bits; b is the base format and n is the number in the specified base. The base format is a one or two character code that signifies the following types of numbers:

b	unsigned binary
o	unsigned octal
d	unsigned decimal
h	unsigned hexadecimal
sb	signed binary
so	signed octal
sd	signed decimal
sh	signed hexadecimal

In hexadecimal numbers the letters a through f represent the digits 10 through 15. Letters in integer constants can be either lower or upper case.

Examples:

63 — unsized unsigned decimal number

'd63 — unsized unsigned decimal number

'h3f — unsized unsigned hexadecimal number

'o77 — unsized unsigned octal number

'b11_1111 — unsized unsigned binary number

12'h3f — 12 bit unsigned hexadecimal number

5'sd0 — 5 bit signed decimal number

The letters x and z can be given to denote unknown and high impedance digits in all numbers that use a base format, and _ is ignored. Sized constants for which the size is larger than the given number are padded on the left with zeros unless the first digit of the given number is an x or z, which are padded with the x or z. The number is truncated on the left if the size is smaller than the given number.

Examples:

64'o0 — a 64 bit octal 0 (zero padded)

8'hx — equivalent to 8'bxxxx_xxxx (x padded)

12'hfx — equivalent to 12'b0000_1111_xxxx (zero padded)

8'hfffx — equivalent to 8'b1111_xxxx (truncated)

Real Numbers

Real numbers must either include a decimal point or a scale factor. If a decimal point is present, there must be digits on both sides. So .12, 9., 4.eE3, and .2e-7 are not valid numbers. Underscores are ignored in real numbers. Scale factors are given in the table below. These scale factors are available in Verilog-A and Verilog-AMS, but not in Verilog.

Examples:

3.14

0.1

1.2E12

1.30e-2

236.123_763e-12

1.3u

5.46K

Scale factors for real numbers.

Multiplier	Name	Symbol
1012	tera	T
109	giga	G
106	mega	M
103	kilo	K or k
10-3	milli	m
10-6	micro	u
10-9	nano	n
10-12	pico	p
10-15	fempto	f
10-18	atto	a
10d	exponent	e d or E d

constants.vams

Predefined numbers in the form of compiler directives are included in the file constants.vams and listed in the table below (only available in Verilog-A and Verilog-AMS). The would be included with:

`include "constants.vams"

Mathematical constants are denoted with a `M_ prefix.

Predefined mathematical constants in constants.vams

`M_PI	π	3.14159265358979323846
`M_TWO_PI	2π	6.28318530717958647693
`M_PI_2	π/2	1.57079632679489661923
`M_PI_4	π/4	0.78539816339744830962
`M_1_PI	1/π	0.31830988618379067154
`M_2_PI	2/π	0.63661977236758134308
`M_2_SQRTPI	2/√π	1.12837916709551257390
`M_E	e	2.7182818284590452354
`M_LOG2E	log2 e	1.4426950408889634074
`M_LOG10E	log10 e	0.43429448190325182765
`M_LN2	loge 2	0.69314718055994530942
`M_LN10	loge 10	2.30258509299404568402
`M_SQRT2	√2	1.41421356237309504880
`M_SQRT1_2	1/√2	0.70710678118654752440

Physical constants use the `P_ prefix.

Predefined physical constants in constants.vams

`P_Q	charge of an electron	1.602176462 × 10 -19 C
`P_C	speed of light	2.99792458 × 10 8 m/s
`P_K	Boltzmann’s constant	1.3806503 × 10 -23 J/K
`P_H	Planck’s constant	6.626076 × 10 -34 J-s
`P_EPS0	permittivity of a vacuum	8.854187817 × 10 -12 F/m
`P_U0	permeability of a vacuum	4π10 -7 H/m
`P_CELSIUS0	0 Celsius	273.15 K