Verilog基础知识（有符号数运算规则，加减运算，乘法运算中的符号位拓展问题）

太过爱你忘了你带给我的痛 2022-04-24 21:24 163阅读 0赞

[https://blog.csdn.net/maxwell2ic/article/details/80620991][https_blog.csdn.net_maxwell2ic_article_details_80620991]

rule of thumb

The format of the signed type is two’s complement. 有符号数均为补码表示  
If any operand in an expression is unsigned the operation is considered to be unsigned. 只有计算表达式右边有无符号数，整个计算式都按照无符号数规则运算  
只有算式右边全为有符号数，运算才会自动补齐所需的bit数，n+n=n+1.n\*n=2n  
The value -4 represented as a 3bit signed hex value would be specified as -3’sh4. A decimal number is always signed. verilog2001中用’s来特别声明有符号数，十进制的数都是有符号数  
Type casting using $unsigned will make the operation unsigned. The operand will be sign extended with 0’s if necessary. $usigned()函数在高位补0  
A=$signed(B) will extend using sign bit. $unsigned()函数会在高位补与符号位相同的bit  
basic signed addition

两个n bit数相加，得到n+1 bit结果，比如-2(3’sb110)+3(3’sb011)=1(4’sb0011)

//Code Example 1: Addition - Verilog 1995  
module add\_signed\_1995 (  
input \[2:0\] A,  
input \[2:0\] B,  
output \[3:0\] Sum  
);  
assign Sum = \{A\[2\],A\} + \{B\[2\],B\};  
endmodule // add\_signed\_1995  
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//Code Example 2: Addition - Verilog 2001  
module add\_signed\_2001 (  
input signed \[2:0\] A,  
input signed \[2:0\] B,  
output signed \[3:0\] Sum  
);  
assign Sum = A + B;  
endmodule // add\_signed\_2001  
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signed + unsigned

如果是两个3bit有符号数+1bit进位。如果在verilog2001中直接用符号位拓展

sum=A+B+carry\_in //整个计算式会转换成无符号计算,signed to unsigned conversion occurs  
sum=A+B+$signed(carry\_in) //就会出现当carry\_in=1时候拓展为4'b1111，这时候本来是加1，却变成了减1  
sum = A + B + $signed(\{1'b0,carry\_in\}) //正确的做法  
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正确的做法是

// Code Example 3: Add with Carry - Verilog 1995  
module add\_carry\_signed\_1995 (  
input \[2:0\] A,dsa  
input \[2:0\] B,  
input carry\_in,  
output \[3:0\] Sum  
);  
assign Sum = \{A\[2\],A\} + \{B\[2\],B\} + carry\_in;  
endmodule //add\_carry\_signed\_1995  
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// Code Example 5: Add with Carry - Correct  
module add\_carry\_signed\_final (  
input signed \[2:0\] A,  
input signed \[2:0\] B,  
input carry\_in,  
output signed \[3:0\] Sum  
);  
assign Sum = A + B + $signed(\{1'b0,carry\_in\});  
endmodule // add\_carry\_signed\_final  
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basic signed multiplication

两个n bit数相乘，得到2n bit结果。如果-3(3’sb101) \* 2 (3’sb010) 得到正确结果 -6 (6’sb111010)。但如果乘数是负数，则最高位的乘积需要以减法参与运算，而不是加法。

// Code Example 6: Signed Multiply - Verilog 1995  
module mult\_signed\_1995 (  
input \[2:0\] a,  
input \[2:0\] b,  
output \[5:0\] prod  
);  
wire \[5:0\] prod\_intermediate0;  
wire \[5:0\] prod\_intermediate1;  
wire \[5:0\] prod\_intermediate2;  
wire \[2:0\] inv\_add1;  
assign prod\_intermediate0 = b\[0\] ? \{ \{3\{a\[2\]\}\}, a\} : 6'b0;  
assign prod\_intermediate1 = b\[1\] ? \{ \{2\{a\[2\]\}\}, a, 1'b0\} : 6'b0;  
// Do the invert and add1 of a.  
assign inv\_add1 = ~a + 1'b1;  
assign prod\_intermediate2 = b\[2\] ? \{ \{1\{inv\_add1\[2\]\}\},  
inv\_add1, 2'b0\} : 6'b0;  
assign prod = prod\_intermediate0 + prod\_intermediate1 +  
prod\_intermediate2;  
endmodule  
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// Code Example 7: Signed Multiply - Verilog 2001  
module mult\_signed\_2001 (  
input signed \[2:0\] a,  
input signed \[2:0\] b,  
output signed \[5:0\] prod  
);  
assign prod = a\*b;  
endmodule  
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signed \* unsigned

prod = a\*b; //整个运算变成无符号，-3(3'sb101)\*2(3'b010)变成5(6'b000101)\*2(6'b000010)=10(6'b001010)  
prod = a\*$signed(b); //当乘数的MSB=1的时候会出错，-2(3'sb010)\*7(3'b111)变成  
//-2(6'sb000010)\*-1(6'sb111111)=2(6'sb110010)  
prod = a\*$signed(\{1'b0,b\}); //正确做法  
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// Code Example 11: Signed by Unsigned Multiply  
module mult\_signed\_unsigned\_2001 (  
input signed \[2:0\] a,  
input \[2:0\] b,  
output signed \[5:0\] prod  
);  
assign prod = a\*$signed(\{1'b0,b\});  
endmodule  
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signed shift

逻辑移位’>>’, ‘<<’会补零，算术移位’<<<’, ‘>>>’会补符号位

A = 8'sb10100011  
A>>3; //8'b00010100  
A>>>3; //8'b11110100  
\---------------------  
作者：maxwell2ic  
来源：CSDN  
原文：https://blog.csdn.net/maxwell2ic/article/details/80620991  
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[https_blog.csdn.net_maxwell2ic_article_details_80620991]: https://blog.csdn.net/maxwell2ic/article/details/80620991