Question:
If x = (1111)2, y = (1001)2 and z = (110)2, then what is x3 – y3 – z3 – 3xyz equal to?
If x = (1111)2, y = (1001)2 and z = (110)2, then what is x3 – y3 – z3 – 3xyz equal to?
Options:
- a) (1111001)2
- b) (1001111)2
- c) (1)2
- d) (0)2
- a) (1111001)2
- b) (1001111)2
- c) (1)2
- d) (0)2
correct answer : d)
Explanation:
x = (1111)2 = 23 + 22 + 21 + 1 = 15
y = (1001)2 = 23 + 0 + 0 + 1 = 9
z = (110)2 = 22 + 21 + 0 = 6
Now, x3 – y3 – z3 – 3xyz
= (15)3 – (9)3 – (6)3 – 3 × 15 × 9 × 6
= 3375 – 729 – 216 – 2430
= 0
x = (1111)2 = 23 + 22 + 21 + 1 = 15
y = (1001)2 = 23 + 0 + 0 + 1 = 9
z = (110)2 = 22 + 21 + 0 = 6
Now, x3 – y3 – z3 – 3xyz
= (15)3 – (9)3 – (6)3 – 3 × 15 × 9 × 6
= 3375 – 729 – 216 – 2430
= 0