计算机系统要素-第二章 布尔运算

1 本章构建完整的算术逻辑单元ALU。
2 有符号的二进制数
    1) 补码：x的补码=2的n次方-x，即反码+1
    2) 减法可以看成x-y=x+(-y)
3 加法器
    1) HalfAdder 半加器
        /**
         * Computes the sum of two bits.
         */
       
        CHIP HalfAdder {
            IN a, b;    // 1-bit inputs
            OUT sum,    // Right bit of a + b
                carry;  // Left bit of a + b
       
            PARTS:
            Xor(a=a,b=b,out=sum);
            And(a=a,b=b,out=carry);
        }
       
    2) FullAdder 全加器
        /**
         * Computes the sum of three bits.
         */
       
        CHIP FullAdder {
            IN a, b, c;  // 1-bit inputs
            OUT sum,     // Right bit of a + b + c
                carry;   // Left bit of a + b + c
       
            PARTS:
            HalfAdder(a=a,b=b,sum=s1,carry=c1);
            HalfAdder(a=s1,b=c,sum=sum,carry=c2);
            Or(a=c1,b=c2,out=carry);
        }
   
    3) Add16 加法器
        /**
         * Adds two 16-bit values.
         * The most significant carry bit is ignored.
         */
       
        CHIP Add16 {
            IN a[16], b[16];
            OUT out[16];
       
            PARTS:
            HalfAdder(a=a[0],b=b[0],sum=out[0],carry=c1);
            FullAdder(a=a[1],b=b[1],c=c1,sum=out[1],carry=c2);
            FullAdder(a=a[2],b=b[2],c=c2,sum=out[2],carry=c3);
            FullAdder(a=a[3],b=b[3],c=c3,sum=out[3],carry=c4);
            FullAdder(a=a[4],b=b[4],c=c4,sum=out[4],carry=c5);
            FullAdder(a=a[5],b=b[5],c=c5,sum=out[5],carry=c6);
            FullAdder(a=a[6],b=b[6],c=c6,sum=out[6],carry=c7);
            FullAdder(a=a[7],b=b[7],c=c7,sum=out[7],carry=c8);
            FullAdder(a=a[8],b=b[8],c=c8,sum=out[8],carry=c9);
            FullAdder(a=a[9],b=b[9],c=c9,sum=out[9],carry=c10);
            FullAdder(a=a[10],b=b[10],c=c10,sum=out[10],carry=c11);
            FullAdder(a=a[11],b=b[11],c=c11,sum=out[11],carry=c12);
            FullAdder(a=a[12],b=b[12],c=c12,sum=out[12],carry=c13);
            FullAdder(a=a[13],b=b[13],c=c13,sum=out[13],carry=c14);
            FullAdder(a=a[14],b=b[14],c=c14,sum=out[14],carry=c15);
            FullAdder(a=a[15],b=b[15],c=c15,sum=out[15],carry=c16);
       
        }
    4) Inc16 增量器
        /**
         * 16-bit incrementer:
         * out = in + 1 (arithmetic addition)
         */
       
        CHIP Inc16 {
            IN in[16];
            OUT out[16];
       
            PARTS:
            Add16(a=in,b[1..15]=false,b[0]=true,out=out);
        }
       
4 算术逻辑单元ALU
    1) ALU
        /**
         * The ALU (Arithmetic Logic Unit).
         * Computes one of the following functions:
         * x+y, x-y, y-x, 0, 1, -1, x, y, -x, -y, !x, !y,
         * x+1, y+1, x-1, y-1, x&y, x|y on two 16-bit inputs,
         * according to 6 input bits denoted zx,nx,zy,ny,f,no.
         * In addition, the ALU computes two 1-bit outputs:
         * if the ALU output == 0, zr is set to 1; otherwise zr is set to 0;
         * if the ALU output < 0, ng is set to 1; otherwise ng is set to 0.
         */
       
        // Implementation: the ALU logic manipulates the x and y inputs
        // and operates on the resulting values, as follows:
        // if (zx == 1) set x = 0        // 16-bit constant
        // if (nx == 1) set x = !x       // bitwise not
        // if (zy == 1) set y = 0        // 16-bit constant
        // if (ny == 1) set y = !y       // bitwise not
        // if (f == 1)  set out = x + y  // integer 2‘s complement addition
        // if (f == 0)  set out = x & y  // bitwise and
        // if (no == 1) set out = !out   // bitwise not
        // if (out == 0) set zr = 1
        // if (out < 0) set ng = 1
       
        CHIP ALU {
            IN 
                x[16], y[16],  // 16-bit inputs       
                zx, // zero the x input?
                nx, // negate the x input?
                zy, // zero the y input?
                ny, // negate the y input?
                f,  // compute out = x + y (if 1) or x & y (if 0)
                no; // negate the out output?
       
            OUT
                out[16], // 16-bit output
                zr, // 1 if (out == 0), 0 otherwise
                ng; // 1 if (out < 0),  0 otherwise
       
            PARTS:
            Mux16(a=x,b[0..15]=false,sel=zx,out=x1);   
            Not16(in=x1,out=nx1);
            Mux16(a=x1,b=nx1,sel=nx,out=x2);
           
            Mux16(a=y,b[0..15]=false,sel=zy,out=y1);   
            Not16(in=y1,out=ny1);
            Mux16(a=y1,b=ny1,sel=ny,out=y2);
               
            Add16(a=x2,b=y2,out=o1);
            And16(a=x2,b=y2,out=o2);
           
            Mux16(a=o2,b=o1,sel=f,out=o3);
           
            Not16(in=o3,out=no3);
            Mux16(a=o3,b=no3,sel=no,out=o4);        
           
            And16(a[0..15]=true,b=o4,out=out);
            Or16Way(in=o4,out=o5);
            Not(in=o5,out=zr);
            And16(a=o4,b[0..14]=false,b[15]=true,out=ng1);   
            Or16Way(in=ng1,out=ng);   
        }