Discrete Mathematics: Home Work #5
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Discrete Mathematics
Home Work #5
Q#1) Use Prime factorization to find a) gcd(1, 5).
b) gcd(100, 101).
c) gcd(123, 277).
d) gcd(1529, 14039).
Q#2) Use the Euclidean algorithm to find a) gcd(1, 5).
b) gcd(100, 101).
c) gcd(123, 277).
d) gcd(1529, 14039).
e) gcd(1529, 14038).
f ) gcd(11111, 111111).
Q#3) Use the Euclidean algorithm to find a) gcd(12, 18).
b) gcd(111, 201).
c) gcd(1001, 1331).
d) gcd(12345, 54321).
e) gcd(1000, 5040).
f ) gcd(9888, 6060).
Q#4) Find LCM of the following:a) lcm(12, 18).
b) lcm(111, 201).
c) lcm(1001, 1331).
d) lcm(12345, 54321).
e) lcm(1000, 5040).
f ) lcm(9888, 6060).
Q#5) Find gcd(92928, 123552) and lcm(92928, 123552), and verify that gcd(92928, 123552) ・ lcm(92928, 123552) = 92928 ・ 123552
Q#6) Evaluate these quantities. a) −17 mod 2
b) 144 mod 7
c) −101 mod 13
d) 199 mod 19
Q#7) Evaluate these quantities. a) 13 mod 3
b) −97 mod 11
c) 155 mod 19
d) −221 mod 23
Q#8) Given the two binary numbers X = 11110100 and Y = 10010110, perform the subtraction, using 2’s complements a)X – Y
b) Y – X
Q#9) Given the two binary numbers X = 11110000 and Y = 10111111, perform the subtraction, using 2’s complements a)X – Y
b) Y – X
Q#9) Represent the following signed numbers using 2 bytes registers (16 bits) using 2’s complement only 1) (+1325) 2) (-1325) 3) (+120) 4) (-120) 5) (-1) 6) (+1)
Home Work #5
Q#1) Use Prime factorization to find a) gcd(1, 5).
b) gcd(100, 101).
c) gcd(123, 277).
d) gcd(1529, 14039).
Q#2) Use the Euclidean algorithm to find a) gcd(1, 5).
b) gcd(100, 101).
c) gcd(123, 277).
d) gcd(1529, 14039).
e) gcd(1529, 14038).
f ) gcd(11111, 111111).
Q#3) Use the Euclidean algorithm to find a) gcd(12, 18).
b) gcd(111, 201).
c) gcd(1001, 1331).
d) gcd(12345, 54321).
e) gcd(1000, 5040).
f ) gcd(9888, 6060).
Q#4) Find LCM of the following:a) lcm(12, 18).
b) lcm(111, 201).
c) lcm(1001, 1331).
d) lcm(12345, 54321).
e) lcm(1000, 5040).
f ) lcm(9888, 6060).
Q#5) Find gcd(92928, 123552) and lcm(92928, 123552), and verify that gcd(92928, 123552) ・ lcm(92928, 123552) = 92928 ・ 123552
Q#6) Evaluate these quantities. a) −17 mod 2
b) 144 mod 7
c) −101 mod 13
d) 199 mod 19
Q#7) Evaluate these quantities. a) 13 mod 3
b) −97 mod 11
c) 155 mod 19
d) −221 mod 23
Q#8) Given the two binary numbers X = 11110100 and Y = 10010110, perform the subtraction, using 2’s complements a)X – Y
b) Y – X
Q#9) Given the two binary numbers X = 11110000 and Y = 10111111, perform the subtraction, using 2’s complements a)X – Y
b) Y – X
Q#9) Represent the following signed numbers using 2 bytes registers (16 bits) using 2’s complement only 1) (+1325) 2) (-1325) 3) (+120) 4) (-120) 5) (-1) 6) (+1)
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