1 Is 3e2e 3 divisible by 7 2 Verify the following statement

1. Is 3e(2e + 3) divisible by 7? 2. Verify the following statements a) 100 = 5(mod 5) b) 112 = 4(mod 7) c) 80 = 8(mod 2) 3.Howmanyelementsareinthesetf3,4,3,5,2,8, 4,5,8,9)? 4. Using 8-bit representation compute the following sums a) 111+45 b) 67 +67 5. Using a Caesar cipher decrypt the following message and determine the key used. (Hint: OnIy O or E can be doubled together, Alphabet wraps around) LXX MABL UHHD BL WHGX Hint: Find the common letters. 6. Let A = { 4, 5, 6, 7 , 8) and B = { 2 , 6, 8). Draw the arrow diagrams for P and Q such that the relationship follows: (x,y) E P means that x

Solution

Ans 4:-

converting 111 to 8 bit

111=64+32+4+2+1=2^6+2^5+2^2+2^1+2^0=01101111

similarly,45=00101101

01101111

+00101101

ans=10011100

that is 2^7+2^4+2^3+2^2=156