Hi,

First, I would like to design a two level circuit that accepts a 4bit input string and determines if it is a palindrome.

Second, I would also like to implement this 4bit detection system using a 8x1 multiplexer with 3 control lines and 8 input lines.

I have not been able to find much information on the internet. Can you help me draw the two circuits? Thanks in advance.

 

I must be missing something, so let me re-phrase the first part of the question. If the four bits are binary, i.e., 0-15, and you exclude the trivial answers, there is only one palindrome in that sequence, namely 11. Now, if you look at the binary, eleven is not a palindrome, but six, nine, and 15 (and zero) are.

So, in what base do you want the palindrome to be defined? Are you referring to numbers or words?

The simplest circuit I can think of right now would involve microcontroller, such as as PIC 16F628A, but there are many other possibilities. Are you willing to use software or do you want a hardware solution?

John

 

Sorry I did not make my question clear enough. I would like to check for a palindrome in base 2 using logic gates. I would prefer not to use xor gates in the circuit.

Example of what I would like to do:

Input: 1101 Output: 0 (not a palindrome)
Input: 1001 Output: 1 (palindrome)
Input: 1111 Ouptut: 1 (palindrome)
Input: 1010 Output: 0 (not a palindrome)

 

For 4-bit binary palindrome detection, you could XNOR bits 1&4, XNOR bits 2&3 then AND the two results.

 

I got the truth table:

Input Output
0000 1
0001 0
0010 0
0011 0
0100 0
0101 0
0110 1
0111 0
1000 0
1001 0
1010 0
1011 0
1100 0
1101 0
1110 0
1111 1



I dont have any Xnor or Xor gates so I would need a solution that does not use them.

 

You could make XNOR from NAND gates.

 

I got the truth table:

Input Output
0000 1
0001 0
0010 0
0011 0
0100 0
0101 0
0110 1
0111 0
1000 0
1001 1
1010 0
1011 0
1100 0
1101 0
1110 0
1111 1



I dont have any Xnor or Xor gates so I would need a solution that does not use them.

Shouldn't you include 1001 as one of the palindromes?

hgmjr

 

You can construct and XOR function using inverters and OR gates.

hgmjr

 

See: http://www.allaboutcircuits.com/vol_4/chpt_7/7.html

Or, see p. 491 in Horowitz and Hill.

John

 

Shouldn't you include 1001 as one of the palindromes?

hgmjr

I made a mistake typing. From the truth table I get the boolean equation
F=A'B'C'D'+A'BCD'+AB'C'D+ABCD

I got the circuit figure out. I am not sure how to solve the problem with the 8-1 mux and ideas on how I should set it up?

 

Still having problems with how to implement this 4bit detection system using a 8x1 multiplexer with 3 control lines and 8 input lines. Any help with that or resources that can help me? Thanks.

 

You could easily do it with a 16x1 mux (four address lines) or two each 1x8 muxes (with some unused lines in one mux). I really don't think it can be done with a single 8x1 mux. You can't represent a four digit number with three digits.