How to install 64-bit .deb file on a 32-bit machine?

Provided that your hardware support 64-bits, which does:

CPU op-mode(s): 32-bit, 64-bit

and the package was prepared to use multiarch, which is also true:

 dpkg -I viber.deb
 new debian package, version 2.0. <--- here
 size 57046082 bytes: control archive=8024 bytes.
       0 bytes,     0 lines      0                    
    1210 bytes,    29 lines      control              
    9475 bytes,    33 lines   *  copyright            
    7404 bytes,    85 lines      md5sums              
      39 bytes,     2 lines   *  postinst             #!/bin/bash
     800 bytes,    35 lines   *  preinst              #!/bin/bash
     500 bytes,    24 lines   *  prerm                #!/bin/bash
 Package: viber
 Version: 4.2.2.6
 Section: non-free/net
 Priority: extra
 Architecture: amd64 <---- and here

you could just install the necessary 64-bit libraries and binaries which are dependency of the package (which is none, more about that later) that you need to run the application, with virtual zero performance impact. In my case, I just installed the package just fine:

$ sudo dpkg --add-architecture amd64
## adding 64-bits architecture package, in my system I didn't need to
## but it's likely you have
$ sudo apt-get update # this downloads the package list for amd64 arch
$ sudo dpkg -i viber.deb
Selecting previously unselected package viber.
(Reading database ... 268703 files and directories currently installed.)
Preparing to unpack viber.deb ...
Unpacking viber (4.2.2.6) ...
Setting up viber (4.2.2.6) ...
Processing triggers for hicolor-icon-theme (0.13-1) ...
Processing triggers for gnome-menus (3.13.3-1) ...
Processing triggers for mime-support (3.56) ...
Processing triggers for desktop-file-utils (0.22-1) ...

And then started running into problems...

The package managers decided that they should not list any dependency for their package,

 Installed-Size: 141336
 Conflicts: Viber (<< 4.2.2.6)
 Replaces: Viber (<< 4.2.2.6)
 Maintainer: Viber Media Inc <[email protected]>

which they actually need:

ldd /opt/viber/Viber | grep 'not found'
    libXcomposite.so.1 => not found
    libxslt.so.1 => not found
    libxml2.so.2 => not found
    libgstreamer-0.10.so.0 => not found
    libgstapp-0.10.so.0 => not found
    libgstbase-0.10.so.0 => not found
    libgstinterfaces-0.10.so.0 => not found
    libgstpbutils-0.10.so.0 => not found
    libgstvideo-0.10.so.0 => not found
    libsqlite3.so.0 => not found

so you must find and install the libraries missing manually! This is easy if you know the correct tools. apt-file comes handy here, also http://packages.ubuntu.com functionality "Search the contents of packages" comes fine also. But I went ahead and searched for them:

These files are already installed in my system, you only need to copy the package name, the one before the colon that ends with amd64. You should copy the package names as they are:

dpkg -S $(ldd /opt/viber/Viber | awk '{print $3}' | grep -vP 'not|viber')
libc6:amd64: /lib/x86_64-linux-gnu/libpthread.so.0
libc6:amd64: /lib/x86_64-linux-gnu/libdl.so.2
libc6:amd64: /lib/x86_64-linux-gnu/librt.so.1
libstdc++6:amd64: /usr/lib/x86_64-linux-gnu/libstdc++.so.6
libc6:amd64: /lib/x86_64-linux-gnu/libm.so.6
libgcc1:amd64: /lib/x86_64-linux-gnu/libgcc_s.so.1
libc6:amd64: /lib/x86_64-linux-gnu/libc.so.6
libx11-6:amd64: /usr/lib/x86_64-linux-gnu/libX11.so.6
libxext6:amd64: /usr/lib/x86_64-linux-gnu/libXext.so.6
zlib1g:amd64: /lib/x86_64-linux-gnu/libz.so.1
libgl1-mesa-glx:amd64: /usr/lib/x86_64-linux-gnu/libGL.so.1
libxrender1:amd64: /usr/lib/x86_64-linux-gnu/libXrender.so.1
libglib2.0-0:amd64: /lib/x86_64-linux-gnu/libglib-2.0.so.0
libglib2.0-0:amd64: /usr/lib/x86_64-linux-gnu/libgobject-2.0.so.0
libxcb1:amd64: /usr/lib/x86_64-linux-gnu/libxcb.so.1
libglapi-mesa:amd64: /usr/lib/x86_64-linux-gnu/libglapi.so.0
libxdamage1:amd64: /usr/lib/x86_64-linux-gnu/libXdamage.so.1
libxfixes3:amd64: /usr/lib/x86_64-linux-gnu/libXfixes.so.3
libx11-xcb1:amd64: /usr/lib/x86_64-linux-gnu/libX11-xcb.so.1
libxcb-glx0:amd64: /usr/lib/x86_64-linux-gnu/libxcb-glx.so.0
libxcb-dri2-0:amd64: /usr/lib/x86_64-linux-gnu/libxcb-dri2.so.0
libxcb-dri3-0:amd64: /usr/lib/x86_64-linux-gnu/libxcb-dri3.so.0
libxcb-present0:amd64: /usr/lib/x86_64-linux-gnu/libxcb-present.so.0
libxcb-sync1:amd64: /usr/lib/x86_64-linux-gnu/libxcb-sync.so.1
libxshmfence1:amd64: /usr/lib/x86_64-linux-gnu/libxshmfence.so.1
libxxf86vm1:amd64: /usr/lib/x86_64-linux-gnu/libXxf86vm.so.1
libdrm2:amd64: /usr/lib/x86_64-linux-gnu/libdrm.so.2
libpcre3:amd64: /lib/x86_64-linux-gnu/libpcre.so.3
libffi6:amd64: /usr/lib/x86_64-linux-gnu/libffi.so.6
libxau6:amd64: /usr/lib/x86_64-linux-gnu/libXau.so.6
libxdmcp6:amd64: /usr/lib/x86_64-linux-gnu/libXdmcp.so.6

These I didn't had them installed, which I obtained using ldd /opt/viber/Viber | grep 'not found' | awk '{printf "%s$\n", $1}' | apt-file search -x -a amd64 -f - | sed 's/\:/:amd64:/':

$ ldd /opt/viber/Viber | grep 'not found' | awk '{printf "%s$\n", $1}' | apt-file search -x -a amd64 -f - | sed 's/\:/:amd64:/'
libgstreamer-plugins-base0.10-0:amd64: /usr/lib/x86_64-linux-gnu/libgstapp-0.10.so.0
libgstreamer-plugins-base0.10-0:amd64: /usr/lib/x86_64-linux-gnu/libgstinterfaces-0.10.so.0
libgstreamer-plugins-base0.10-0:amd64: /usr/lib/x86_64-linux-gnu/libgstpbutils-0.10.so.0
libgstreamer-plugins-base0.10-0:amd64: /usr/lib/x86_64-linux-gnu/libgstvideo-0.10.so.0
libgstreamer0.10-0:amd64: /usr/lib/x86_64-linux-gnu/libgstbase-0.10.so.0
libgstreamer0.10-0:amd64: /usr/lib/x86_64-linux-gnu/libgstreamer-0.10.so.0
libsqlite3-0:amd64: /usr/lib/x86_64-linux-gnu/libsqlite3.so.0
libxcomposite1:amd64: /usr/lib/x86_64-linux-gnu/libXcomposite.so.1
libxml2:amd64: /usr/lib/x86_64-linux-gnu/libxml2.so.2
libxslt1.1:amd64: /usr/lib/x86_64-linux-gnu/libxslt.so.1

apt-file was a tease to give me the 64-bit packages so I had to do sudo apt-file -a amd64 update to force it to have the 64-bit file list.

Now, let me explain what is all the above:

• ldd /path/to/binary: reads a binary and tells you what are the required libraries, symbols, etc.
• dpkg -S: search which packages provide a specific installed file.
• awk, sed and grep: are modifying the text stream to process only the interesting parts or show the desired output.
• |, $(...): the first allows me to pipe the output of a command to another, and the later allows me to execute/evaluate a command before the main ones gets executed.

TL;dr just install these packages:

sudo dpkg --add-architecture amd64 ## adding 64-bits architecture package
sudo apt-get update
sudo apt-get install libgstreamer-plugins-base0.10-0:amd64 libgstreamer-plugins-base0.10-0:amd64 libgstreamer-plugins-base0.10-0:amd64 libgstreamer-plugins-base0.10-0:amd64 libgstreamer0.10-0:amd64 libgstreamer0.10-0:amd64 libsqlite3-0:amd64 libxcomposite1:amd64 libxml2:amd64 libxslt1.1:amd64 libc6:amd64 libdrm2:amd64 libffi6:amd64 libgcc1:amd64 libgl1-mesa-glx:amd64 libglapi-mesa:amd64 libglib2.0-0:amd64 libpcre3:amd64 libstdc++6:amd64 libx11-6:amd64 libx11-xcb1:amd64 libxau6:amd64 libxcb1:amd64 libxcb-dri2-0:amd64 libxcb-dri3-0:amd64 libxcb-glx0:amd64 libxcb-present0:amd64 libxcb-sync1:amd64 libxdamage1:amd64 libxdmcp6:amd64 libxext6:amd64 libxfixes3:amd64 libxrender1:amd64 libxshmfence1:amd64 libxxf86vm1:amd64 zlib1g:amd64

You also need to install the 64-bit kernel.

It is not possible to install a software which support only 64 bit arch on a 32 bit OS whereas the reverse is true. In order to install a 64 bit software you will need a hardware which support 64 bit and a 64 bit OS running on the top of it.

Also I would like to mention that it is not possible to install 64 Bit OS as a Virtual machine on a hardware which support only 32 bit architecture. Your hardware should support 64 Bit architecture along with virtualization support in order to create 64 Bit virtual machines.

I have to say you are not true about

my computer only supports 32-bit

According to the output of running lscpu your Ubuntu version that installed is 32 bit while Your system can support 64 bit application if you want to install 64 bit application you have to install 64 bit of Ubuntu OS. see this lines below:

Architecture: i686              # <-- your kernel is 32 bit (32 bit Ubuntu)
CPU op-mode(s): 32-bit, 64-bit  # <-- your cpu can handle 32 or 64 bit instructions
Byte Order: Little Endian
CPU(s): 2
On-line CPU(s) list: 0,1
Thread(s) per core: 1 
Core(s) per socket: 2 
Socket(s): 1 
Vendor ID: GenuineIntel 
CPU family: 6 
Model: 23 
Stepping: 10 
CPU MHz: 2800.000 
BogoMIPS: 5586.12 
Virtualization: VT-x 
L1d cache: 32K 
L1i cache: 32K 
L2 cache: 2048K

Download and install 64 bit Ubuntu 14.04.1 and then install Viber as well.