• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
    • Theories
    • Rule-classes
    • Proof-builder
    • Recursion-and-induction
    • Hons-and-memoization
    • Events
    • Parallelism
    • History
    • Programming
      • Defun
      • Declare
      • System-utilities
      • Stobj
      • State
      • Mutual-recursion
      • Memoize
      • Mbe
      • Io
      • Defpkg
      • Apply$
      • Loop$
      • Programming-with-state
      • Arrays
      • Characters
      • Time$
      • Defmacro
      • Loop$-primer
      • Fast-alists
      • Defconst
      • Evaluation
      • Guard
      • Equality-variants
      • Compilation
      • Hons
      • ACL2-built-ins
      • Developers-guide
      • System-attachments
      • Advanced-features
      • Set-check-invariant-risk
      • Numbers
      • Efficiency
      • Irrelevant-formals
      • Introduction-to-programming-in-ACL2-for-those-who-know-lisp
      • Redefining-programs
      • Lists
      • Invariant-risk
      • Errors
      • Defabbrev
      • Conses
      • Alists
      • Set-register-invariant-risk
      • Strings
        • Std/strings
        • String-listp
        • Stringp
        • Length
        • Search
        • Remove-duplicates
        • Position
        • Coerce
        • Concatenate
        • Reverse
        • String
        • Subseq
        • Substitute
        • String-upcase
        • String-downcase
        • Count
        • Char
        • String<
        • String-equal
        • String-utilities
          • Code-char-injectivity-theorem
          • 8bitbytes-hexchars-conversions
            • Ubyte8s=>hexchars
            • Hexchars=>ubyte8s
            • Ubyte8=>hexchars
              • Ubyte8<=>hexchars-inverses-theorems
            • Hexchars=>ubyte8
          • Code-char-inverses-theorems
          • String-kinds
          • String-codelist-conversions
          • Charlist-codelist-conversions
          • 8bitbytes-hexstrings-conversions
        • String-append
        • String>=
        • String<=
        • String>
        • Hex-digit-char-theorems
        • String-downcase-gen
        • String-upcase-gen
      • Program-wrapper
      • Get-internal-time
      • Basics
      • Packages
      • Oracle-eval
      • Defmacro-untouchable
      • <<
      • Primitive
      • Revert-world
      • Unmemoize
      • Set-duplicate-keys-action
      • Symbols
      • Def-list-constructor
      • Easy-simplify-term
      • Defiteration
      • Fake-oracle-eval
      • Defopen
      • Sleep
    • Operational-semantics
    • Real
    • Start-here
    • Debugging
    • Miscellaneous
    • Output-controls
    • Macros
    • Interfacing-tools
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• 8bitbytes-hexchars-conversions

Ubyte8=>hexchars

Convert an unsigned 8-bit byte to two hexadecimal digit characters.

Signature

(ubyte8=>hexchars byte) → (mv hi-char lo-char)

Arguments

byte — Guard (unsigned-byte-p 8 byte).

Returns

hi-char — Type (str::hex-digit-char-p hi-char).

lo-char — Type (str::hex-digit-char-p lo-char).

The most significant digit comes first, followed by the least significant one. If the byte is below 16, the first digit is zero. The hexadecimal digits above 9 are uppercase letters.

Definitions and Theorems

Function: ubyte8=>hexchars

(defun ubyte8=>hexchars (byte)
  (declare (xargs :guard (unsigned-byte-p 8 byte)))
  (let ((__function__ 'ubyte8=>hexchars))
    (declare (ignorable __function__))
    (b* ((byte (mbe :logic (unsigned-byte-fix 8 byte)
                    :exec byte)))
      (mv (str::hex-digit-to-char (floor byte 16))
          (str::hex-digit-to-char (mod byte 16))))))

Theorem: hex-digit-char-p-of-ubyte8=>hexchars.hi-char

(defthm hex-digit-char-p-of-ubyte8=>hexchars.hi-char
  (b* (((mv ?hi-char ?lo-char)
        (ubyte8=>hexchars byte)))
    (str::hex-digit-char-p hi-char))
  :rule-classes :rewrite)

Theorem: hex-digit-char-p-of-ubyte8=>hexchars.lo-char

(defthm hex-digit-char-p-of-ubyte8=>hexchars.lo-char
  (b* (((mv ?hi-char ?lo-char)
        (ubyte8=>hexchars byte)))
    (str::hex-digit-char-p lo-char))
  :rule-classes :rewrite)

Theorem: mv-nth-0-of-ubyte8=>hexchars-of-unsigned-byte-fix

(defthm mv-nth-0-of-ubyte8=>hexchars-of-unsigned-byte-fix
  (equal (mv-nth 0
                 (ubyte8=>hexchars (unsigned-byte-fix 8 byte)))
         (mv-nth 0 (ubyte8=>hexchars byte))))

Theorem: mv-nth-1-of-ubyte8=>hexchars-of-unsigned-byte-fix

(defthm mv-nth-1-of-ubyte8=>hexchars-of-unsigned-byte-fix
  (equal (mv-nth 1
                 (ubyte8=>hexchars (unsigned-byte-fix 8 byte)))
         (mv-nth 1 (ubyte8=>hexchars byte))))

Subtopics

Ubyte8<=>hexchars-inverses-theorems

ubyte8=>hexchars and hexchars=>ubyte8 are mutual inverses.