can anyone helps me to solve all these questions, please Solve the following con
ID: 2883473 • Letter: C
Question
can anyone helps me to solve all these questions, please
Solve the following congruences. Make sure your answer includes the mod and that the numerical solution begins with the smallest number within the mod.
11. 6x - 2 ? 8 mod 8
4x + 3 ? 8 mod 11
Convert the following octal number to hexadecimal.
3478
Add in the indicated bases.
6358 + 4748
1100110102 + 110101112
Subtract in the indicated bases.
C0A16 - BCF16
11000012 - 1101012
Convert from the base indicated directly to decimal.
2548
3it6 3i + 6
Explanation / Answer
6x-2 = 8 mod 8 = 16 mod 8 (since 0,8,16 are equivalent under mod 8)
6x -2 =16 gives x = 3
Next solution is 6x-2 = 16+24 =40
x = 7
Hence solutions would be 3, 7, 11,.....
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4x+3 = 8 mod 11 and x is an integer
4x+3 =8 gives x in fraction. Next 4x+3 = 19 gives x = 4
Next is 4x+3 = 19+44 = 63
gives x = 15 , and so on.
Hence solutins are 4, 15, 26, 37,....
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3478 =3(83) +4(82) + 7(8) +8
= 1536+256+56+8
= 1856 in decimal.
1856 in powers of 16 would be
256(7)+64
= 162(7) + 16(4)
Hence in dexadecimal equal to 74
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