Odd-Numbered Binary Inputs & XOR Gates

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SUMMARY

The discussion focuses on using 2-input XOR gates to achieve a high output when an odd number of bits are high in a four-bit binary input. The proposed method involves grouping the four bits into two pairs and utilizing XOR gates to determine the output based on specific input conditions. The circuit design requires careful consideration of input combinations, specifically when one bit from a pair is high while the other is low, or both bits from the other pair are high. Additionally, the implementation of AND or NAND gates using XOR gates is suggested as part of the solution.

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  • Understanding of 2-input XOR gate functionality
  • Basic knowledge of digital circuit design
  • Familiarity with binary number representation
  • Concept of AND and NAND gate operations
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The discussion is beneficial for electronics enthusiasts, theoretical physicists venturing into circuit design, and students studying digital logic design who want to understand the application of XOR gates in binary input scenarios.

sos617@bham.a
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Hi i am a theoretical physicist and am trying to understand electronics. (not a very bright idea)
basically my question is how can we use 2 input xor gates to give a high output when an odd number of bits are high in a four bit binary. also what would such a circuit look like.
 
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Start with a piece of paper and work out which combinations of inputs you want the output on for.
For simplicity consider the 4bits as two pairs of bits.
Then you want an output when either there is only one of the first pair and none of the second or both of the second. (and vice versa)
hint - if either both or none of a pair is on then an XOR would be false.

You will probably also have to work out how to implement an AND (or NAND) from XOR.
 
Or, you may simply route two lines to one XOR, and the other two to another XOR (it doesn't matter which lines), and then take the two XOR outputs to a third XOR.

KM
 

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