Is there a way to tell whether my CPU is 64-bit or 32-bit?
The best way to find out whether your CPU is 64-bit or 32-bit is by using lscpu command. Here is an output of lscpu command:
$ lscpu 
Architecture:          x86_64
CPU op-mode(s):        32-bit, 64-bit
Byte Order:            Little Endian
CPU(s):                4
On-line CPU(s) list:   0-3
Thread(s) per core:    2
Core(s) per socket:    2
Socket(s):             1
NUMA node(s):          1
Vendor ID:             GenuineIntel
CPU family:            6
Model:                 42
Model name:            Intel(R) Core(TM) i7-2640M CPU @ 2.80GHz
Stepping:              7
CPU MHz:               800.078
CPU max MHz:           3500.0000
CPU min MHz:           800.0000
BogoMIPS:              5581.80
Virtualization:        VT-x
L1d cache:             32K
L1i cache:             32K
L2 cache:              256K
L3 cache:              4096K
NUMA node0 CPU(s):     0-3

From the above lscpu command output we can see that architecture currently in use is x86_64 and CPU is capable operating in both 32-bit, 64-bit modes. Below is a lscpu output of a regular 32-bit CPU:
$ lscpu 
Architecture:          i686
CPU op-mode(s):        32-bit
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:                 14
Stepping:              12
CPU MHz:               1000.000
BogoMIPS:              3325.11
Virtualisation:        VT-x
L1d cache:             32K
L1i cache:             32K
L2 cache:              2048K
The above lscpu command output reports that this processor is only capable to operate in 32-bit instruction mode. In the next example you can see 64-bit CPU running 32-bit Linux:
# lscpu 
Architecture:          i686
CPU op-mode(s):        32-bit, 64-bit
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:                 15
Stepping:              6
CPU MHz:               1000.000
BogoMIPS:              2992.54
Virtualization:        VT-x
L1d cache:             32K
L1i cache:             32K
L2 cache:              4096K


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