Circuits:Karnaugh Map to Circuit

一、3-variable

This section talks about the expression obtained through Karnaugh map simplification
This question is simplified

• RTL代码

module top_module(
    input a,
    input b,
    input c,
    output out  ); 

    assign out = ~(~a & ~b & ~c);
        
endmodule

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二、4-variable

Karnaugh map simplification result is

• RTL代码

module top_module(
    input a,
    input b,
    input c,
    input d,
    output out  ); 
    
    assign out = ( ~a & ~b & ~c) | (a & ~b & ~c) | (~a & ~d) | (b & c & d) | (a & ~b & d);

endmodule

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三、4-variable

Karnaugh map reduces to（Pay attention to the numbers on the outer row,有陷阱）

• RTL代码

module top_module(
    input a,
    input b,
    input c,
    input d,
    output out  ); 
    
    assign out = a | (~b & c);

endmodule

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四、4-variable

• RTL代码

module top_module(
    input a,
    input b,
    input c,
    input d,
    output out  );
    
    assign out = (~a&~b&~c&d)|(~a&b&~c&~d)|(a&b&~c&d)|(a&~b&~c&~d)|(~a&b&c&d)|(a&~b&c&d)|(~a&~b&c&~d)|(a&b&c&~d);

endmodule

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五、Minimum SOP and POS

SOP是以1The center circle is the Carnot circle,POS是以0The center circle is the Carnot circle,Both use the same Karnaugh map.

• RTL代码

module top_module (
    input a,
    input b,
    input c,
    input d,
    output out_sop,
    output out_pos
); 
    assign out_sop = (c & d) | (~a & ~b &c);
    assign out_pos = c & (~b | d) & (~a | d);

endmodule

六、Karnaugh map

• RTL代码

module top_module (
    input [4:1] x, 
    output f );
    
    assign f = (x[2] & x[4]) | (x[3] & x[4]) | (~x[1] & x[3]);

endmodule

七、Karnaugh map

• RTL代码

module top_module (
    input [4:1] x,
    output f
); 
    assign f = (~x[2] & ~x[4]) | (~x[1] & x[3]) | (x[2] & x[3] & x[4]);

endmodule

八、K-map implemented with a multiplexer

• RTL代码

module top_module (
    input c,
    input d,
    output [3:0] mux_in
); 

    assign mux_in[0] = c | d;
    assign mux_in[1] = 1'b0;
    assign mux_in[2] = ~d;
    assign mux_in[3] = c & d;

endmodule

• 仿真波形图