Is it possible to make a circuit that can convert binary to decimal

binarydecimal

I know that computers use binary to calculate instructions and perform tasks. But essentially no one I know can convert binary to decimal. I am working on a calculator project currently, and the problem I have is converting binary to decimal for display and utilitarianism. But all of the converting circuits I have seen have converted it into hexadecimal instead, and no one knows how to read hex either. How can I convert binary to decimal and vice versa?

Best Answer

Yes, it is possible.

If your input is straight binary (not BCD) and all you have is transistors and logic gates then you will need to start by creating the truth tables for the function you need. The inputs to the truth tables will be the bits of the binary value; the outputs will be the bits of the decimal value.

Once you have the truth tables you can try to use Karnaugh maps or Quine-McCluskey techniques for minimization.

Another alternative would be to use your transistors to build a ROM that did the conversion. The address lines to the ROM would be your binary bits and the data lines coming out would be the desired decimal bits.

Either way, you should probably sharpen your wirestrippers first.

Related Solutions

Decimal-Binary-Hex-Base7 Conversions with Radix Points

I think I spotted it:

DecToBase7(0.25) = (0*7^0)+(2*7^-1)+(5*7^-2) = (0) + (0.2857142857) + (0.1020408163) = 0.387755102 or by specs 0.3877.

Yes, that is how I convert a 0.25_(base 7) to a base-ten decimal value.

To convert 8.8750_(decimal) to a base-7 value, you need to go the other way:

8.8750_(decimal)                            1
                                            1
                                            .
0.8750_(decimal) * 7 = 6.1250_(decimal) --> 6
0.1250_(decimal) * 7 = 0.8750_(decimal) --> 0
0.8750_(decimal) * 7 = 6.1250_(decimal) --> 6
0.1250_(decimal) * 7 = 0.8750_(decimal) --> 0
0.8750_(decimal) * 7 = 6.1250_(decimal) --> 6
0.1250_(decimal) * 7 = 0.8750_(decimal) --> 0
0.8750_(decimal) * 7 = 6.1250_(decimal) --> 6
...                               ...

So 8.8750_(decimal) is equal to 11.60606060606...(base 7).

With a few special exceptions, converting a fraction in any one base to a fraction in any other base usually leads to such repeating patterns. (Perhaps the most notorious such unexpected repeating pattern happens when converting 0.1_(decimal) to binary. A similar repeating pattern occurs when converting 0.1_(base 3) to decimal).

Adding/Subtracting in binary and hexadecimal formats

M - N can be done in the usual way as:

  00111100110100.1011 -  
  10010001111101.1010 
---------------------
1 10101010110111.0001
---------------------

We have a borrow here. Answer is negative and is in 2's complement form.

Or you can add the 2's complement of N with M.

-N = 2's complement of N = 101101110000010.0110

 0 00111100110100.1011 +  
 1 01101110000010.0110 
  ---------------------
 1 10101010110111.0001
  ---------------------

Take the 2's complement of this number to get -01010101001000.1111 = -5448.9375.

Best Answer

Related Solutions

Decimal-Binary-Hex-Base7 Conversions with Radix Points

Adding/Subtracting in binary and hexadecimal formats

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