Odd-Numbered Binary Inputs & XOR Gates

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In summary, the conversation discusses using 2 input XOR gates to produce a high output when an odd number of bits are high in a four bit binary. The suggestion is to start with a piece of paper and determine which combinations of inputs would result in the desired output. Additionally, the conversation suggests using XOR gates to implement an AND or NAND function.
  • #1
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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  • #2
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.
 
  • #3
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
 

1. What is an odd-numbered binary input?

An odd-numbered binary input is a sequence of binary digits (0 or 1) that contains an odd number of 1s. For example, 1011 is an odd-numbered binary input because it has three 1s.

2. What is an XOR gate?

An XOR gate is a type of logic gate that performs an exclusive OR operation on two binary inputs. It outputs a 1 if the two inputs are different, and a 0 if they are the same. XOR gates are commonly used in digital circuits for data encryption and error detection.

3. How does an XOR gate work?

An XOR gate works by comparing two binary inputs and producing an output based on the following logic: if the two inputs are different, the output will be 1. If the two inputs are the same, the output will be 0. This can be represented using a truth table, where 1 represents true and 0 represents false.

4. What is the significance of using odd-numbered binary inputs with XOR gates?

Using odd-numbered binary inputs with XOR gates can help to create more complex and secure digital circuits. By using an odd number of 1s in the input, the output of the XOR gate will be unpredictable and difficult to replicate, making it useful for data encryption and error detection.

5. What are some applications of odd-numbered binary inputs and XOR gates?

Odd-numbered binary inputs and XOR gates have various applications in digital circuits, including data encryption, error detection and correction, parity checking, and digital signal processing. They are also commonly used in computer hardware, such as CPUs and memory modules.

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