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<HTML><HEAD> <META NAME="GENERATOR" CONTENT="Adobe PageMill 2.0 Mac"> <LINK REL="STYLESHEET" HREF="ch02.css"> <TITLE> 2.5 Numbers </TITLE></HEAD><BODY BGCOLOR="#ffffff"><P><A NAME="pgfId=212"></A><HR ALIGN=LEFT></P><P><A HREF="ch02.htm">Chapter start</A> <A HREF="ch02.4.htm">Previous page</A> <A HREF="ch02.6.htm">Next page</A></P><H1>2.5 Numbers</H1><P><P CLASS="Body"><A NAME="pgfId=5085"></A><I>Constant numbers</I> canbe specified as integer constants or real constants.</P><PRE><A NAME="pgfId=5248"></A> number ::= decimal_number | octal_number| binary_number| hex_number| real_number<A NAME="pgfId=5249"></A> decimal_number ::= [ sign ] unsigned_number| [ size ] decimal_base unsigned_number<A NAME="pgfId=5250"></A> binary_number ::= [ size ] binary_base binary_digit {<B> _</B> | binary_digit }<A NAME="pgfId=5251"></A> octal_number ::= [ size ] octal_base octal_digit {<B> _</B> | octal_digit }<A NAME="pgfId=5252"></A> hex_number ::= [ size ] hex_base hex_digit {<B> _</B> | hex_digit }<A NAME="pgfId=5253"></A> real_number ::= [ sign ] unsigned_number <B>.</B> unsigned_number | [ sign ] unsigned_number [ <B>.</B> unsigned_number ] <B>e</B> [ sign ] unsigned_number | [ sign ] unsigned_number [ <B>.</B> unsigned_number ] <B>E</B> [ sign ] unsigned_number<A NAME="pgfId=5254"></A> sign ::= <B>+</B> | <B>-</B><A NAME="pgfId=5255"></A> size ::= unsigned_number<A NAME="pgfId=5256"></A> unsigned_number ::= decimal_digit {<B> _</B> | decimal_digit }<A NAME="pgfId=5257"></A> decimal_base ::= <B>'d</B> | <B>'D</B><A NAME="pgfId=5258"></A> binary_base ::= <B>'b</B> | <B>'B</B><A NAME="pgfId=5259"></A> octal_base ::= <B>'o</B> | <B>'O</B><A NAME="pgfId=5260"></A> hex_base ::= <B>'h</B> | <B>'H</B><A NAME="pgfId=5261"></A> decimal_digit ::= <B>0</B> | <B>1</B> | <B>2</B> | <B>3</B> | <B>4</B> | <B>5</B> | <B>6</B> | <B>7</B> | <B>8</B> | <B>9</B><ANAME="pgfId=5262"></A> binary_digit ::= <B>x</B> | <B>X</B> | <B>z</B> | <B>Z</B> | <B>0</B> | <B>1</B><ANAME="pgfId=5263"></A> octal_digit ::= <B>x</B> | <B>X</B> | <B>z</B> | <B>Z</B> | <B>0</B> | <B>1</B> |<B> 2</B> | <B>3</B> | <B>4</B> | <B>5</B> | <B>6</B> | <B>7</B><ANAME="pgfId=5264"></A> hex_digit ::= <B>x</B> | <B>X</B> | <B>z</B> | <B>Z</B> | <B>0</B> | <B>1</B> |<B> 2</B> | <B>3</B> | <B>4</B> | <B>5</B> | <B>6</B> | <B>7</B> | <B>8</B> | <B>9</B> | <B>a</B> |<B> b</B> | <B>c</B> | <B>d</B> | <B>e</B> | <B>f</B> | <B>A</B> | <B>B</B> | <B>C</B> | <B>D</B> | <B>E</B> | <B>F</B><ANAME="pgfId=5396"></A></PRE><P><P CLASS="BNFCapBody">Syntax 2-1: Syntax for integer and real numbers</P><P><P CLASS="SubSection"><A NAME="pgfId=5109"></A>Integer constants</P><P><P CLASS="Body"><A NAME="pgfId=310"></A><I>Integer constants</I> canbe specified in decimal, hexadecimal, octal, or binary format.</P><P><P CLASS="Body"><A NAME="pgfId=314"></A>There are two forms to expressinteger constants. The first form is a simple decimal number which shallbe specified as a sequence of digits <CODE>0</CODE> through <CODE>9</CODE>, optionally starting with a plus or minus unary operator. The second formspecifies a <I>sized constant</I> , which shall be composed of up to threetokens - an optional size constant, a single quote followed by a base formatcharacter, and the digits representing the value of the number.</P><P><P CLASS="Body"><A NAME="pgfId=219"></A>The first token, a size constant,shall specify the size of the constant in terms of its exact number of bits.It shall be specified as an unsigned decimal number. For example, the sizespecification for two hexadecimal digits is 8, because one hexadecimal digitrequires four bits.</P><P><P CLASS="Body"><A NAME="pgfId=299"></A>The second token, a base_format,shall consist of a letter specifying the base for the number, preceded bythe single quote character (<CODE> '</CODE> ). Legal base specificationsare <CODE>d</CODE> , <CODE>D</CODE> , <CODE>h</CODE> , <CODE>H</CODE> ,<CODE>o</CODE> , <CODE>O</CODE> , b, or <CODE>B</CODE> , for the bases decimal,hexadecimal, octal, and binary respectively.</P><P><P CLASS="Body"><A NAME="pgfId=216"></A>The use of <CODE>x</CODE> and<CODE>z</CODE> in defining the value of a number is case insensitive.</P><P><P CLASS="Body"><A NAME="pgfId=302"></A>The single quote and the baseformat character shall not be separated by any white space.</P><P><P CLASS="Body"><A NAME="pgfId=217"></A>The third token, an unsignednumber, shall consist of digits that are legal for the specified base format.The unsigned number token shall immediately follow the base format, optionallypreceded by white space. <EM>The hexadecimal digits </EM><CODE>a</CODE><EM>to </EM><CODE>f</CODE> <EM>shall be case insensitive.</EM></P><P><P CLASS="Body"><A NAME="pgfId=325"></A>Simple decimal numbers withoutthe size and the base format shall be treated as <I>signed integers</I>, whereas the numbers specified with the base format shall be treated as<I>unsigned integers</I> .</P><P><P CLASS="Body"><A NAME="pgfId=225"></A>A plus or a minus operator precedingthe size constant is a sign for the constant number; the size constant doesnot take a sign. A plus or minus operator between the base format and thenumber is an illegal syntax.</P><P><P CLASS="Body"><A NAME="pgfId=308"></A><I>Negative numbers</I> shallbe represented in 2's complement form.</P><P><P CLASS="Body"><A NAME="pgfId=229"></A>An <CODE>x</CODE> representsthe <I>unknown value</I> in hexadecimal, octal, and binary constants<CODE>.</CODE> A <CODE>z</CODE> represents the <I>high impedance</I> value. Seesection 3.1 for a discussion of the Verilog HDL value set. An <CODE>x</CODE>shall set four bits to unknown in the hexadecimal base, three bits in theoctal base, and one bit in the binary base. Similarly, a <CODE>z</CODE>shall set four, three, and one bit, respectively, to the high impedancevalue.</P><P><P CLASS="Body"><A NAME="pgfId=300"></A>If the size of the unsigned numberis smaller than the size specified for the constant, the unsigned numbershall be padded to the left with zeros. If the left most bit in the unsignednumber is an <CODE>x</CODE> or a <CODE>z</CODE> , then an <CODE>x</CODE>or a <CODE>z</CODE> shall be used to pad to the left respectively.</P><P><P CLASS="Body"><A NAME="pgfId=232"></A>When used in a number, the questionmark <CODE>(?)</CODE> character is a Verilog HDL alternative for the <CODE>z</CODE>character. It sets four bits to the high impedance value in hexadecimalnumbers, three in octal, and one in binary. The question mark can be usedto enhance readability in cases where the high impedance value is a don't-carecondition. See the discussion of <B>casez</B> <EM>and </EM><B>casex</B>insection 9.5.1. The question mark character is also used in user definedprimitive state table. See section 8.1.4.</P><P><P CLASS="Body"><A NAME="pgfId=274"></A>The underscore character (_)shall be legal anywhere in a number except as the first or the last character.This feature can be used to break up long numbers for readability purposes.</P><P><P CLASS="Body"><A NAME="pgfId=220"></A>Examples:</P><P><P CLASS="Body"><A NAME="pgfId=175"></A>Unsized constant numbers</P><P><P CLASS="Body"><A NAME="pgfId=5269"></A>659 // is a decimal number <BR>'h 837FF // is a hexadecimal number <BR>'o7460 // is an octal number <BR>4af // is illegal (hexadecimal format requires 'h)</P><P><P CLASS="Body"><A NAME="pgfId=223"></A>Sized constant numbers</P><P><P CLASS="CodeText"><A NAME="pgfId=5287"></A>4'b1001 // is a 4-bit binarynumber <BR>5 'D 3 // is a 5-bit decimal number <BR>3'b01x // is a 3-bit number with the least <BR>// significant bit unknown <BR>12'hx // is a 12-bit unknown number <BR>16'hz // is a 16-bit high impedance number</P><P><P CLASS="Body"><A NAME="pgfId=226"></A>Using sign with constant numbers</P><P><P CLASS="CodeText"><A NAME="pgfId=5297"></A>8 'd -6 // thisis illegal syntax <BR>-8 'd 6 // this defines the two's complement of 6, <BR> // held in 8 bits--equivalent to -(8'd 6)</P><P><P CLASS="Body"><A NAME="pgfId=208"></A>Automatic left padding</P><P><P CLASS="CodeText"><A NAME="pgfId=5307"></A><B>reg</B> [11:0] a, b,c, d;<BR><B>initial begin<BR></B>a = 'h x; // yields xxx<BR>b = 'h 3x; // yields 03x<BR>c = 'h z3; // yields zz3<BR>d = 'h 0z3; // yields 0z3<BR><B>end</B></P><P><P CLASS="Body"><A NAME="pgfId=227"></A>Using underscore character innumbers</P><P><P CLASS="CodeText"><A NAME="pgfId=5317"></A>27_195_000 <BR>16'b0011_0101_0001_1111 <BR>32 'h 12ab_f001</P><P><P CLASS="Note"><A NAME="pgfId=234"></A>NOTES</P><OL> <P><P CLASS="NumberedNote1"><A NAME="pgfId=209"></A>1) --A sized negative number is not sign-extended when assigned to a register data type. <P><P CLASS="NumberedNote2"><A NAME="pgfId=218"></A>2) --Each of the three tokens for specifying a number may be macro substituted. <P><P CLASS="NumberedNote2"><A NAME="pgfId=171"></A>3) --The number of bits that make up an unsized number (which is a simple decimal number or a number without the size specification) shall be at least 32.</OL><P><P CLASS="SubSection"><A NAME="pgfId=172"></A>Real constants</P><P><P CLASS="Body"><A NAME="pgfId=176"></A>The <I>real constant numbers</I>shall be represented as described by IEEE STD-754-1985, an IEEE standardfor double precision floating point numbers.</P><P><P CLASS="Body"><A NAME="pgfId=316"></A>Real numbers can be specifiedin either decimal notation (for example, 14.72) or in scientific notation(for example, 39e8, which indicates 39 multiplied by 10 to the 8th power).Real numbers expressed with a decimal point shall have at least one digiton each side of the decimal point.</P><P><P CLASS="Body"><A NAME="pgfId=317"></A>Examples:</P><PRE><A NAME="pgfId=318"></A> 1.2 0.1 2394.26331 1.2E12 (the exponent symbol can be e or E) 1.30e-2 0.1e-0 23E10 29E-2 236.123_763_e-12 (underscores are ignored)</PRE><P><P CLASS="Body"><A NAME="pgfId=319"></A>The following are invalid formsof real numbers because they do not have at least one digit on each sideof the decimal point:</P><PRE><A NAME="pgfId=320"></A> .12 9.4.E3 .2e-7</PRE><P><P CLASS="SubSection"><A NAME="pgfId=321"></A>Conversion</P><P><P CLASS="Body"><A NAME="pgfId=322"></A>Real numbers shall be convertedto integers by rounding the real number to the nearest integer, rather thanby truncating it. Implicit conversion shall take place when a real numberis assigned to an integer. The ties shall be rounded away from zero.</P><P><P CLASS="Body"><A NAME="pgfId=324"></A>Examples:</P><P><P CLASS="Body"><A NAME="pgfId=326"></A>The real numbers 35.7 and 35.5both become 36 when converted to an integer and 35.2 becomes 35.</P><P><P CLASS="Body"><A NAME="pgfId=328"></A>Converting -1.5 to integer yields-2, converting 1.5 to integer yields 2.</P><P><HR ALIGN=LEFT></P><P><A HREF="ch02.htm">Chapter start</A> <A HREF="ch02.4.htm">Previous page</A> <A HREF="ch02.6.htm">Next page</A></BODY></HTML>⌨️ 快捷键说明
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