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to Binary in the Common Lisp Track

Published at Nov 27 2019 · 0 comments
Instructions
Test suite
Solution

Convert a binary number, represented as a string (e.g. '101010'), to its decimal equivalent using first principles.

Implement binary to decimal conversion. Given a binary input string, your program should produce a decimal output. The program should handle invalid inputs.

Note

  • Implement the conversion yourself. Do not use something else to perform the conversion for you.

About Binary (Base-2)

Decimal is a base-10 system.

A number 23 in base 10 notation can be understood as a linear combination of powers of 10:

  • The rightmost digit gets multiplied by 10^0 = 1
  • The next number gets multiplied by 10^1 = 10
  • ...
  • The nth number gets multiplied by 10^(n-1).
  • All these values are summed.

So: 23 => 2*10^1 + 3*10^0 => 2*10 + 3*1 = 23 base 10

Binary is similar, but uses powers of 2 rather than powers of 10.

So: 101 => 1*2^2 + 0*2^1 + 1*2^0 => 1*4 + 0*2 + 1*1 => 4 + 1 => 5 base 10.

Setup

Check out Installing Common Lisp for instructions to get started or take a look at the guides available in the track's side bar.

Formatting

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VIM

Use the following commands to ensure VIM uses only spaces for indentation:

:set tabstop=2
:set shiftwidth=2
:set expandtab

(or as a oneliner :set tabstop=2 shiftwidth=2 expandtab). This can be added to your ~/.vimrc file to use it all the time.

Emacs

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(setq-default indent-tabs-mode nil)

This can be placed in your ~/.emacs (or ~/.emacs.d/init.el) in order to have it set whenever Emacs is launched.

One suggested add-on for Emacs and Common Lisp is SLIME which offers tight integration with the REPL; making iterative coding and testing very easy.

Source

All of Computer Science http://www.wolframalpha.com/input/?i=binary&a=*C.binary-_*MathWorld-

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

binary-test.lisp

(ql:quickload "lisp-unit")
#-xlisp-test (load "binary")

(defpackage #:binary-test
  (:use #:common-lisp #:lisp-unit))

(in-package #:binary-test)

(define-test binary-1-is-decimal-1
  (assert-equal 1 (binary:to-decimal "1")))

(define-test binary-10-is-decimal-2
  (assert-equal 2 (binary:to-decimal "10")))

(define-test binary-11-is-decimal-3
  (assert-equal 3 (binary:to-decimal "11")))

(define-test binary-100-is-decimal-4
  (assert-equal 4 (binary:to-decimal "100")))

(define-test binary-1001-is-decimal-9
  (assert-equal 9 (binary:to-decimal "1001")))

(define-test binary-11010-is-decimal-26
  (assert-equal 26 (binary:to-decimal "11010")))

(define-test binary-10001101000-is-decimal-1128
  (assert-equal 1128 (binary:to-decimal "10001101000")))

(define-test invalid-binary-is-decimal-0
  (assert-equal 0 (binary:to-decimal "carrot")))

(define-test invalid-characters-at-beginning
  (assert-equal 2 (binary:to-decimal "a10")))

(define-test invalid-characters-at-end
  (assert-equal 2 (binary:to-decimal "10a")))

(define-test invalid-characters-in-middle
  (assert-equal 2 (binary:to-decimal "1a0")))

(define-test invalid-digits
  (assert-equal 0 (binary:to-decimal "23")))

#-xlisp-test
(let ((*print-errors* t)
      (*print-failures* t))
  (run-tests :all))
(defpackage #:binary
  (:use #:common-lisp)
  (:export #:to-decimal))

(in-package #:binary)

(defun to-decimal (str)
  (let ((pos 1))
    (reduce
      (lambda (s e)
        (when (find e "01")
          (incf s (* (digit-char-p e) pos))
          (setf pos (* pos 2)))
        s)
      (reverse str)
      :initial-value 0)))

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