diff --git a/Library/Homebrew/extend/os/linux/install.rb b/Library/Homebrew/extend/os/linux/install.rb
index bb830d2dc1a65..7940896db0144 100644
--- a/Library/Homebrew/extend/os/linux/install.rb
+++ b/Library/Homebrew/extend/os/linux/install.rb
@@ -16,7 +16,8 @@ module Install
     ].freeze
 
     def check_cpu
-      return if (Hardware::CPU.intel? && Hardware::CPU.is_64_bit?) || Hardware::CPU.arm?
+      return if Hardware::CPU.intel? && Hardware::CPU.is_64_bit?
+      return if Hardware::CPU.arm?
 
       message = "Sorry, Homebrew does not support your computer's CPU architecture!"
       if Hardware::CPU.ppc64le?
diff --git a/Library/Homebrew/extend/os/mac/hardware/cpu.rb b/Library/Homebrew/extend/os/mac/hardware/cpu.rb
index da5c4c5345f9d..fad0ba4ce52dd 100644
--- a/Library/Homebrew/extend/os/mac/hardware/cpu.rb
+++ b/Library/Homebrew/extend/os/mac/hardware/cpu.rb
@@ -1,5 +1,7 @@
 # frozen_string_literal: true
 
+require "macho"
+
 module Hardware
   class CPU
     class << self
diff --git a/Library/Homebrew/install.rb b/Library/Homebrew/install.rb
index 108b51b95cec0..f68572df0845d 100644
--- a/Library/Homebrew/install.rb
+++ b/Library/Homebrew/install.rb
@@ -10,10 +10,13 @@ module Install
     module_function
 
     def check_cpu
-      return if (Hardware::CPU.intel? && Hardware::CPU.is_64_bit?) || Hardware::CPU.arm?
+      return if Hardware::CPU.intel? && Hardware::CPU.is_64_bit?
 
       message = "Sorry, Homebrew does not support your computer's CPU architecture!"
-      if Hardware::CPU.ppc?
+      if Hardware::CPU.arm?
+        opoo message
+        return
+      elsif Hardware::CPU.ppc?
         message += <<~EOS
           For PowerPC Mac (PPC32/PPC64BE) support, see:
             #{Formatter.url("https://github.com/mistydemeo/tigerbrew")}
diff --git a/Library/Homebrew/os/mac/version.rb b/Library/Homebrew/os/mac/version.rb
index 0ca02de626dd4..dd52ffe1c3c58 100644
--- a/Library/Homebrew/os/mac/version.rb
+++ b/Library/Homebrew/os/mac/version.rb
@@ -1,12 +1,13 @@
 # frozen_string_literal: true
 
+require "hardware"
 require "version"
 
 module OS
   module Mac
     class Version < ::Version
       SYMBOLS = {
-        big_sur:     "10.16",
+        big_sur:     Hardware::CPU.arm? ? "11.00" : "10.16",
         catalina:    "10.15",
         mojave:      "10.14",
         high_sierra: "10.13",
diff --git a/Library/Homebrew/os/mac/xcode.rb b/Library/Homebrew/os/mac/xcode.rb
index c01ee433de4b4..4861320b5db33 100644
--- a/Library/Homebrew/os/mac/xcode.rb
+++ b/Library/Homebrew/os/mac/xcode.rb
@@ -13,9 +13,10 @@ module Xcode
       # CI systems have been updated.
       # This may be a beta version for a beta macOS.
       def latest_version
-        latest = "11.5"
+        latest_stable = "11.5"
         case MacOS.version
-        when "10.15" then latest
+        when "11.0", "10.16" then "12.0"
+        when "10.15" then latest_stable
         when "10.14" then "11.3.1"
         when "10.13" then "10.1"
         when "10.12" then "9.2"
@@ -26,7 +27,7 @@ def latest_version
           raise "macOS '#{MacOS.version}' is invalid" unless OS::Mac.prerelease?
 
           # Default to newest known version of Xcode for unreleased macOS versions.
-          latest
+          latest_stable
         end
       end
 
@@ -36,6 +37,7 @@ def latest_version
       # also in beta).
       def minimum_version
         case MacOS.version
+        when "11.0", "10.16" then "12.0"
         when "10.15" then "11.0"
         when "10.14" then "10.2"
         when "10.13" then "9.0"
@@ -173,9 +175,10 @@ def detect_version_from_clang_version
         # installed CLT version. This is useful as they are packaged
         # simultaneously so workarounds need to apply to both based on their
         # comparable version.
-        latest = "11.5"
+        latest_stable = "11.5"
         case (DevelopmentTools.clang_version.to_f * 10).to_i
-        when 110     then latest
+        when 120     then "12.0"
+        when 110     then latest_stable
         when 100     then "10.3"
         when 91      then "9.4"
         when 90      then "9.2"
@@ -186,7 +189,7 @@ def detect_version_from_clang_version
         when 61      then "6.1"
         when 60      then "6.0"
         when 0       then "dunno"
-        else              latest
+        else              latest_stable
         end
       end