一个计算器实现计算须要哪些部件？

运算单元 管制单元 存储（寄存器）输出 输入

明天咱们次要关注后面两者

筹备工作

咱们要有存数据的寄存器
寄存器能够通过列表实现
先看一下咱们的寄存器

((func getEmptyList () (list 0 0 0 0 0 0 0 0))
    (define r-a (mark-list 8))
    (define r-b (mark-list 8))
    (define r-c (mark-list 8))
    (define r-d (mark-list 8))
    (define r-e (mark-list 8))
    (define r-temp (mark-list 8))
    (define r-opt (getEmptyList))
    (define r-zero (getEmptyList))
    (func copy (l r) ((define len (length l))
        (define r-len (length r))
        (for ((i 0) (< i len) (i (+ i 1))) ((list-set! r (- r-len i 1) (list-ref l (- len i 1)))
        ))
    ))
    ; 左移
    (func sl(l num) ((define len (length  l))
        (for((i num)(< i len)(i (+ i 1)))((list-set! l (- i num) (list-ref l i))
        ))
        ; 后几位 是 0
        (for ((i (- len num)) (< i len) (i (+ i 1))) (list-set! l i 0))
    ))
)

计算单元

加法

(define add ((lambda () ((func not-eq (a b) (
            and
            (xand a b)
            (or a b)
        ))
       (func not-eq-and  (a b) ((define j (and a b))
           (define p (not-eq a b))
           (cons j p)
        ))
        (func all-add  (a b j) ((define r1 (not-eq-and a b))
            (define r2 (not-eq-and (cdr r1) j))
            (cons  (or (car r1) (car r2)) (cdr r2))
         ))
         (lambda (l-a l-b l-r) ((define j 0)
            (define cons0 nil)
            (copy r-zero l-r)
            (for ((i (- (length l-a) 1)) (< -1 i) (i (- i 1))) ((set! cons0 (all-add (list-ref l-a i) (list-ref l-b i) j))
                    (set! j (car cons0))
                    (list-set! l-r i (cdr cons0))
                 )
            )
         ))
     ))))
    
)

乘法

((func multi (l-a l-b l-r) (
        ; todo 反对正数运算
         (define j nil)
         (define len (length l-b))
         (define l-0 (mark-list 8))
         (define l-1 (mark-list 8))
         (copy r-zero l-r)
         (for ((i (- len 1)) (< -1 i) (i (- i 1))) ((set! j (- len i 1))
            (if (less? zero (list-ref l-b i)) ((copy l-a l-0)
                   (sl l-0 j)
                   (add l-0 l-r l-1)
                   (copy l-1 l-r)
            ))
         ))
         l-r
     ))
)

正数

(
    ; 正数单元
     (define toNegative(lambda (list l-r) ((add (map (lambda (o) (not o)) list) (map (lambda (o i) (eqv? i (- (length list) 1))) list) l-r)
     )))
)

管制单元

一些布尔逻辑的扩大

((func eq? (a b) (or (and a b) (xor a b)
     ))
     (func eql? (l-a l-b) ((define r 1)
          (for((i 0)(< i (length l-a))(i (+ i 1))) ((set! r (and r (eq? (list-ref l-a i) (list-ref l-b i))))
          ))
          r
     ))
     (func less? (a b) (and (xor a zero) (or b zero)
     ))
     (define-macro if (lambda(p exp) (`(and ,p ,exp)
     )))
)

承受数字和指令

(
    ;5 位长就够了 0 结尾的是数字 1 结尾的是指令 + - * /
    (func inputNumber (l-a l-r) (; r = (r*10)+a
        (define ten (list 0 0 0 0 1 0 1 0))
        (multi l-r ten r-e)
        (add r-e l-a r-temp)
        (copy r-temp l-r)
    ))
    (func clac (l-a l-r) (
        ; 0 + 1 - 2 * 3 /
        (if (eql? l-r (list 0 0 0 1 0 0 0 0)) ((add r-a r-b r-temp)
            (copy r-temp r-a)
        ))
        (if (eql? l-r (list 0 0 0 1 0 0 0 1)) ((toNegative r-a r-e)
             (copy r-e r-a)
             (add r-a r-b r-temp)
             (copy r-temp r-a)
        ))
        (if (eql? l-r (list 0 0 0  1 0 0 1 0)) ((multi r-a r-b r-temp)
            (copy r-temp r-a)
        ))
        (copy l-a l-r)
        (copy r-a r-b)
        (copy r-zero r-a)
    ))
)

输出

((func input (l) ((define car0 (car l))
        (if (eq? zero car0) ((define l0 (getEmptyList))
            (copy l l0)
            (inputNumber l0 r-a)
        ))
        (if (less? zero car0) ((clac l r-opt)
        ))
    ))
)

输入

((func println (x) ((display x)
        (newline)
    ))
    (func show () ((if (eql? r-a r-zero) (println r-b))
        (if (not (eql? r-a r-zero)) (println r-a))
    ))
)

测试

(
    ; 二进制 1 执行后 r-a => 0001
     (input (list 0 0 0 0 1))
    ; 二进制 1 执行后 r-a => 1011
    (input (list 0 0 0 0 1))   
    ; 二进制 执行后 r-opt => 10001 代表 减法，r-a => 0000 r-b => 1011
    (input (list 1 0 0 0 1))
    ; 二进制 11 执行后 r-a => 0011
    (input (list 0 0 0 1 1))
    ; 二进制 执行后 r-opt => 10000 代表 加法，r-a => 11101 r-b => 01011 r-a => 00000 r-b => 01000
    (input (list 1 0 0 0 0))
    (show)
)
=> (#f #f #f #f 1 #f #f #f)

附上全副代码

((func println (x) ((display x)
        (newline)
    ))
    (func ten2two (t) ((define l (mark-list 8))
        (copy r-zero l)
        (define i (length l))
        (while (< 0 t)((set! i (- i 1))
            (list-set! l i (% t 2))
            (set! t (/ t 2))
        ))
        l
    ))
    (func getEmptyList () (list 0 0 0 0 0 0 0 0))
    ; 寄存器 不去实现 用 list 代替 r0-r8 move a b
    (define zero 0)
    (define r-a (mark-list 8))
    (define r-b (mark-list 8))
    (define r-c (mark-list 8))
    (define r-d (mark-list 8))
    (define r-e (mark-list 8))
    (define r-temp (mark-list 8))
    (define r-opt (getEmptyList))
    (define r-zero (list 0 0 0 0 0 0 0 0))
    (func copy (l r) ((define len (length l))
        (define r-len (length r))
        (for ((i 0) (< i len) (i (+ i 1))) ((list-set! r (- r-len i 1) (list-ref l (- len i 1)))
        ))
    ))
    ; 左移
    (func sl(l num) ((define len (length  l))
        (for((i num)(< i len)(i (+ i 1)))((list-set! l (- i num) (list-ref l i))
        ))
        ; 后几位 是 0
        (for ((i (- len num)) (< i len) (i (+ i 1))) (list-set! l i 0))
    ))
     ; 只用 and or not 作为根底
    ;(func and (a b) (and a b))
    ;(func or (a b) (or a b))
    ;(func not (a) (not a))
    (func xor (a b) (not (or a b)))
    (func xand (a b) (not (and a b)))
     ;-- 先实现计算单元
    (define add ((lambda () ((func not-eq (a b) (
            and
            (xand a b)
            (or a b)
        ))
       (func not-eq-and  (a b) ((define j (and a b))
           (define p (not-eq a b))
           (cons j p)
        ))
        (func all-add  (a b j) ((define r1 (not-eq-and a b))
            (define r2 (not-eq-and (cdr r1) j))
            (cons  (or (car r1) (car r2)) (cdr r2))
         ))
         (lambda (l-a l-b l-r) ((define j 0)
            (define cons0 nil)
            (copy r-zero l-r)
            (for ((i (- (length l-a) 1)) (< -1 i) (i (- i 1))) ((set! cons0 (all-add (list-ref l-a i) (list-ref l-b i) j))
                    (set! j (car cons0))
                    (list-set! l-r i (cdr cons0))
                 )
            )
         ))
     ))))
     (func multi (l-a l-b l-r) (
        ; todo 反对正数运算
         (define j nil)
         (define len (length l-b))
         (define l-0 (mark-list 8))
         (define l-1 (mark-list 8))
         (copy r-zero l-r)
         (for ((i (- len 1)) (< -1 i) (i (- i 1))) ((set! j (- len i 1))
            (if (less? zero (list-ref l-b i)) ((copy l-a l-0)
                   (sl l-0 j)
                   (add l-0 l-r l-1)
                   (copy l-1 l-r)
            ))
         ))
         l-r
     ))
     ; 正数单元
     (define toNegative(lambda (list l-r) ((add (map (lambda (o) (not o)) list) (map (lambda (o i) (eqv? i (- (length list) 1))) list) l-r)
     )))
     ;-- 实现管制单元

     (func eq? (a b) (or (and a b) (xor a b)
     ))
     (func eql? (l-a l-b) ((define r 1)
          (for((i 0)(< i (length l-a))(i (+ i 1))) ((set! r (and r (eq? (list-ref l-a i) (list-ref l-b i))))
          ))
          r
     ))
     (func less? (a b) (and (xor a zero) (or b zero)
     ))
     (define-macro if (lambda(p exp) (`(and ,p ,exp)
     )))
     ;5 位长就够了 0 结尾的是数字 1 结尾的是指令 + - * /
    (func inputNumber (l-a l-r) (; r = (r*10)+a
        (define ten (list 0 0 0 0 1 0 1 0))
        (multi l-r ten r-e)
        (add r-e l-a r-temp)
        (copy r-temp l-r)
    ))
    (func clac (l-a l-r) (
        ; 0 + 1 - 2 * 3 /
        (if (eql? l-r (list 0 0 0 1 0 0 0 0)) ((add r-a r-b r-temp)
            (copy r-temp r-a)
        ))
        (if (eql? l-r (list 0 0 0 1 0 0 0 1)) ((toNegative r-a r-e)
             (copy r-e r-a)
             (add r-a r-b r-temp)
             (copy r-temp r-a)
        ))
        (if (eql? l-r (list 0 0 0  1 0 0 1 0)) ((multi r-a r-b r-temp)
            (copy r-temp r-a)
        ))
        (copy l-a l-r)
        (copy r-a r-b)
        (copy r-zero r-a)
    ))
    (func input (l) ((define car0 (car l))
        (if (eq? zero car0) ((define l0 (getEmptyList))
            (copy l l0)
            (inputNumber l0 r-a)
        ))
        (if (less? zero car0) ((clac l r-opt)
        ))
    ))
    (func show () ((if (eql? r-a r-zero) (println r-b))
        (if (not (eql? r-a r-zero)) (println r-a))
    ))

     ; 测试 add
    (copy (list 0 0 0 0 1 0 1 0) r-a)
    (copy (list #f #f #f #f #f #f #f 1) r-b)
    ;(println r-a)
    (add r-a r-b r-c)
   ; (r-a r-b r-c)
    ;(println r-c)
    ; 测试左移
    (define a0 (list 0 0 0 0 0 0 0 1) )
    (sl a0 3)
   ; (println a0)
    ;(println (ten2two 10))
    ; 测试 multi
    (copy r-zero r-c)
    ;(multi  r-b r-a r-c)
    ;(println r-c)
     (copy r-zero r-a)
    (input (list 0 0 0 0 1))
    (input (list 0 0 0 0 1))
    (input (list 1 0 0 0 1))
    (input (list 0 0 0 1 1))
    (input (list 1 0 0 0 0))
    (show)
)

总结

计算的实质是机械性的操作，而如何把这种机械的操作通过机器来实现进去的就是咱们当初看到布尔代数映射到逻辑门的电子计算机，也就是说电子计算机是对机械性操作的的实现之一，有空我会从头开始去讲一下数字到底是什么？进位的益处是什么？数字又是如何计算的? 还有计算是如何通过逻辑与函数形象进去的？
形象的函数又是如何转换为机械性操作的？计算机可否有其余种实现形式？

而 这些最根底的常识只须要初中所学的内容即可，或者咱们能够只须要小学一年级的数学知识