Question

Encryption Computing the XOR computer science

1. Compute the XOR of the following bit strings expressed in hexadecimal, also giving the result in hexadecimal. You may wish to convert to binary first.

a. ff ff ff ff ⊕ de ad be ef

b. 88 88 44 44 ⊕ 77 77 bb bb

c. ca fe fa ce ⊕ 10 45 57 ce

Please do A-C and show the work, thank you.

Answer 1

XOR logic:

Input - Output

0 0  - 0

0 1 - 1

1 0 - 1

1 1 - 0

a)

ff ff ff ff ⊕ de ad be ef

First of all convert to binary

f = 1111

ff ff ff ff = 11111111 11111111 11111111 11111111

d = 1101

e = 1110

a = 1010

b = 1011

f = 1111

de ad be ef = 11011110 10101101 10111110 11101111

Now perform XOR operation

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1

..................................................................................................

0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0

2 = 0010

1 = 0001

5 = 0101

4 = 0100

0 = 0000

(0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0)₂ = 21 52 41 10

b)

88 88 44 44 ⊕ 77 77 bb bb

8 = 1000

4 = 0100

88 88 44 44 = 10001000 10001000 01000100 01000100

7 = 0111

b = 1011

77 77 bb bb = 01110111 01110111 10111011 10111011

Now perform XOR operation

1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0

0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1

...................................................................................................

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  1 1 1 1 1 1 1 1

(1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  1 1 1 1 1 1 1 1)₂ = (ff ff ff ff)₁₆

_c)

ca fe fa ce ⊕ 10 45 57 ce

c = 1100

a = 1010

f = 1111

e= 1110

ca fe fa ce = 11001010 11111110 11111010 11001110

10 45 57 ce

1 = 0001

0 = 0000

4 = 0100

5 = 0101

7 = 0111

c = 1100

e = 1110

10 45 57 ce = 00010000 01000101 01010111 1100 1110

Now perform XOR operation

1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0  1 1 0 0 1 1 1 0

0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0

...................................................................................................

1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0

(1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0)₂ = (da bb ad 00)₁₆