If you're allowed to prove this the easy way (by showing you can use XOR and AND to create the set of AND, OR, and NOT), this is pretty straightforward.
x AND y = x AND y (of course) x OR y = (x XOR y) XOR (x AND y)
NOT x = x XOR 1
Also, (x AND y) XOR 1 is equivalent to x NAND y, which is a universal gate.
A full adder can be constructed using basic logic gates: XOR, AND, and OR gates. Specifically, two XOR gates are used to calculate the sum, while two AND gates and one OR gate are employed to determine the carry-out. The first XOR gate takes the two input bits, and the second XOR gate incorporates the carry-in. The AND gates handle the carry generation, with the OR gate combining the outputs to produce the final carry-out.
And, or, xor, xnor, nand, nor, not
1 gate.
Nand, nor, and, or, xor, nxor, not, true.
X-----Not--------------- | AND----------------| | |------------------ --------- |_ |__________ ---------OR-------OUTPUT | AND-----------------| Y-----|-Not-------------
No, XOR gate is a not a universal gate. There are basically two universal gates NAND and NOR.
Seven gates, they are: not, and, or, nor, nand, xor, xnor.
All other logic gates can be made using XOR and XNOR, but to get NOT, you need to do (input) XOR 1 or (input) XNOR 0, but with NAND, you don't need 1: (input) NAND (input).
The XOR operation can be implemented using only NAND gates by combining multiple NAND gates in a specific arrangement to achieve the desired XOR functionality.
AND OR NOT XOR
yes... xor is derived gate from primary gates
xor and xnor gates are derived from not gate
3*xor- two input
A full adder can be constructed using basic logic gates: XOR, AND, and OR gates. Specifically, two XOR gates are used to calculate the sum, while two AND gates and one OR gate are employed to determine the carry-out. The first XOR gate takes the two input bits, and the second XOR gate incorporates the carry-in. The AND gates handle the carry generation, with the OR gate combining the outputs to produce the final carry-out.
basic gates like XOR already exist in VHDL.
And, or, xor, xnor, nand, nor, not
1 gate.