Consider the set of 64bit long integer numbers denoted by Z64. a) Is Z64 closed under...

Question

Question

Consider the set of 64bit long integer numbers denoted by Z₆₄.

a) Is Z₆₄ closed under XOR operation?

b) Is Z₆₄ closed under AND operation?

c) Is Z₆₄ closed under addition?

engineering Computer-Science

Answer 1

Answer #1

a) true

XOR of two 64 bit numbers will always gives a 64 bit number as xor happens bitwise of the two numbers

b) true

AND of two 64 bit numbers will always gives a 64 bit number as AND happens bitwise of the two numbers

c)false

addition of two 64 bit numbers sometimes gives 65 bit number , so its not closed under addition

take two 3 bit number 6,7

6= 110 in binary

7= 111 in binary

6+7 = 13 (1101) gives 4 bit 13

Answer 2

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