Can I set SASM to show binary representation of the value I have in the registers (eax, ebx..) during debugging along with the hexadecimal and decimal ones?
You can't change the display output of the registers window to display everything in binary. SASM is rather limited.
In the memory and variable window of SASM you can print registers. Registers are specified with a $ sign and the register. To print EAX you'd use $eax and then select bin in the pull down for the type.
Alternatively you can print registers with the GDB command line at the bottom using p /t $eax where EAX is any register. The p command prints, the /t forces binary display.