Architecture 32-bit or 64-bit version

Open a terminal(Ctrl+Alt+T) and type: uname -a

Result for 32-bit Ubuntu:

 Linux discworld 2.6.38-8-generic #42-Ubuntu SMP Mon Apr 11 03:31:50 UTC 2011 i686 i686 i386 GNU/Linux

 whereas the 64-bit Ubuntu will show:

 Linux discworld 2.6.38-8-generic #42-Ubuntu SMP Mon Apr 11 03:31:50 UTC 2011 x86_64 x86_64 x86_64 GNU/Linux

 Shorter version:

$ uname -i

x86_64

or

$ file /sbin/init

Result for 32-bit Ubuntu: /sbin/init: ELF 32-bit LSB shared object, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.15, stripped

 whereas for the 64-bit version it would look like: /sbin/init: ELF 64-bit LSB shared object, x86-64, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.15, stripped

Same for systems using systemd (16.04):

$ file /lib/systemd/systemd

Result for 64-bit: /lib/systemd/systemd: ELF 64-bit LSB shared object, x86-64, version 1 (SYSV), dynamically linked, interpreter /lib64/ld-linux-x86-64.so.2, for GNU/Linux 2.6.32, BuildID[sha1]=54cc7ae53727d3ab67d7ff5d66620c0c589d62f9, stripped