HDLbits 刷题答案 3.1.3 Arithmetic Circuits

3.1.3 Arithmetic Circuits

3.1.3.1 Hadd

module top_module( 
    input a, b,
    output cout, sum );

    assign {cout,sum} = a + b;
endmodule

3.1.3.2 Fadd

module top_module( 
    input a, b, cin,
    output cout, sum );
	
    assign {cout,sum} = a + b + cin;
endmodule

3.1.3.3 3-bit binary adder
1-bit加法器例化成一个3-bit加法器

module top_module( 
    input [2:0] a, b,
    input cin,
    output [2:0] cout,
    output [2:0] sum );
	
    wire tmp1,tmp2,tmp3;
    
    fdder one (a[0],b[0],cin,tmp1,sum[0]);
    fdder two (a[1],b[1],tmp1,tmp2,sum[1]);
    fdder three (a[2],b[2],tmp2,tmp3,sum[2]);
    
    assign cout = {tmp3,tmp2,tmp1};
endmodule

module fdder(
	input a,
    input b,
    input cin,
    output cout,
    output sum
);
    assign {cout,sum} = a + b + cin;
endmodule

3.1.3.4 Adder

module top_module (
    input [3:0] x,
    input [3:0] y, 
    output [4:0] sum);
	
    assign sum = x + y;
endmodule

3.1.3.5 Adder

module top_module (
    input [7:0] a,
    input [7:0] b,
    output [7:0] s,
    output overflow
); //
 	assign s = a + b;
    assign overflow = (a[7] & b[7] & ~s[7]) | (~a[7] & ~b[7] & s[7]);
    // assign s = ...
    // assign overflow = ...

endmodule

a[7]和b[7]分别是两个加数的符号为，s[7]是运算结果的符号位
当a[7] = b[7] = 0（两数同为正数）, s[7]= 1（结果为负数）时，有溢出
当a[7] = b[7] = 1（两数同为负数）, s[7]= 0（结果为正数）时，有溢出
即，若运算结果的符号位与原来加数的符号位不同时，有溢出

3.1.3.6 100-bit binary adder

module top_module( 
    input [99:0] a, b,
    input cin,
    output cout,
    output [99:0] sum );
	
    assign {cout,sum} = a + b + cin;
endmodule

3.1.3.7 4-digital BCD adder

module top_module( 
    input [15:0] a, b,
    input cin,
    output cout,
    output [15:0] sum );

    wire [2:0] tmp;
    
    bcd_fadd adder0 (
        .a(a[3:0]),
        .b(b[3:0]),
        .cin(cin),
        .cout(tmp[0]),
        .sum(sum[3:0])
    );
    
    bcd_fadd adder1 (
        .a(a[7:4]),
        .b(b[7:4]),
        .cin(tmp[0]),
        .cout(tmp[1]),
        .sum(sum[7:4])
    );
    
    bcd_fadd adder2 (
        .a(a[11:8]),
        .b(b[11:8]),
        .cin(tmp[1]),
        .cout(tmp[2]),
        .sum(sum[11:8])
    );
    
    bcd_fadd adder3 (
        .a(a[15:12]),
        .b(b[15:12]),
        .cin(tmp[2]),
        .cout(cout),
        .sum(sum[15:12])
    );

endmodule