A huge number. 0 + 1 + 2 = 3 0 + 2 + 1 = 3 1 + 0 + 2 = 3 1 + 2 + 0 = 3 2 + 0 + 1 = 3 2 + 1 + 0 = 3 -0 + 1 + 2 = 3 -0 + 2 + 1 = 3 1 - 0 + 2 = 31 + 2 - 0 = 32 - 0 + 1 = 32 + 1 - 0 = 3 0 - 1 + 3 = 2 0 + 3 - 1 = 2 -1 + 0 + 3 = 2 -1 + 3 + 0 = 2 3 + 0 - 1 = 2 3 - 1 + 0 = 2 -0 - 1 + 3 = 2-0 + 3 - 1 = 2-1 - 0 + 3 = 2-1 + 3 - 0 = 23 - 0 - 1 = 23 - 1 - 0 = 2 0 - 2 + 3 = 1 0 + 3 - 2 = 1 -2 + 0 + 3 = 1 -2 + 3 + 0 = 1 3 + 0 - 2 = 1 3 - 2 + 0 = 1 -0 - 2 + 3 = 1-0 + 3 - 2 = 1-2 - 0 + 3 = 1-2 + 3 - 0 = 13 - 0 - 2 = 13 - 2 - 0 = 1 1 + 2 - 3 = 0 1 - 3 + 2 = 0 2 + 1 - 3 = 0 2 - 3 + 1 = 0 -3 + 1 + 2 = 0 -3 + 2 + 1 = 0 For each of these equations there is a counterpart in which all signs have been switched. For example 0 + 1 + 2 = 3 gives -0 - 1 - 2 = -3and so on. Now, all of the above equations has three numbers on the left and one on the right. Each can be converted to others with two numbers on each side. For example:the equation 0 + 1 + 2 = 3 gives rise to0 + 1 = 3 - 20 + 1 = -2 + 30 + 2 = 3 - 10 + 2 = -1 + 31 + 2 = 3 - 01 + 2 = -0 + 3-0 + 1 = 3 - 2-0 + 1 = -2 + 3-0 + 2 = 3 - 1-0 + 2 = -1 + 31 + 2 = 3 + 01 + 2 = +0 + 3 As you can see, the number of equations is huge!
the four sets of quantum numbers are: 2, 0, 0, +1/2 2, 0, 0, -1/2 1, 0, 0, +1/2 1, 0, 0, -1/2
Attack Defense Stamina Energy Ring: 1 4 2 Fusion Wheel: 1 4 2 Spin Track: 0 0 2 Performance Tip: 1 5 1 Total: 3 14* 7
1 1/2
E|----------------|-------0-1-0----|----------------|--------1-0-----|--| B|--0-1-----0-1--|--0-1--------1-|------0-1-------|------1----1---|--| G|0-------0------|0--------------2|0-------------0-|-----2-------2-|0-| D|----------------|-----------------|----------------|3--3------------|--| A|----------------|-----------------|----------------|-----------------|--| E|----------------|-----------------|----------------|-----------------|--| E|----3-1---------|-----------------0-|1---------------| B|--------1-------|-----------3-1-----|----------------| G|----------0-----|0-------0----------|----------------| D|------------2-3|----2-3------------|----------------| A|----------------|--------------------|----------------| E|----------------|--------------------|----------------| E|----------------|--------0-1-0----|----------------|-------1-0-----|--| B|--0-1-----0-1-|---0-1-------1--|------0-1-------|------1----1---|--| G|0-------0------|-0--------------2|0------------0-|-----2-------2-|0-| D|----------------|------------------|----------------|3--3-----------|--| A|----------------|------------------|----------------|----------------|--| E|----------------|------------------|----------------|----------------|--|
(2 - 1) * 0 = 0 Thus 2 - 1 = 0/0 = 0 and therefore 2 = 1
There are six total ways: 1-0-1-0=2 1-1-0-0=2 1-0-0-1=2 0-0-1-1=2 0-1-0-1=2 0-1-1-0=2
Given:Length (L) = 10Characters: 0, 1, therefore Count (n) = 25 consecutive zeros or 5consecutiveonesI'll try to map out some logic for you. I'm sorry this took so many edits for me to get the correct answer. These problems can some times be a little tricky, and I just kept tripping up on the logic.:First, calculate the maximum amount of possibilities, without any constants.This step is optional, however it gives you a check on your final answer.Length = 10n = 2Therefore, the maximum amount of possibilities without any constants is 2^10 = 1084. If you get a number higher than 1084, which in one of my edits I did, than your answer is obviously incorrect.Case 1: Fiveconsecutivezeros[0][0][0][0][0][?][?][?][?][?] ==> 2^5 possibilities (2 x 2 x 2 x 2 x 2)[1][0][0][0][0][0][?][?][?][?] ==> 2^4 possibilities[?][1][0][0][0][0][0][?][?][?] ==> 2^4 possibilities[?][?][1][0][0][0][0][0][?][?] ==> 2^4 possibilities[?][?][?][1][0][0][0][0][0][?] ==> 2^4 possibilities[?][?][?][?][1][0][0][0][0][0] ==> 2^4 possibilities (1 possibility duplicated from case 2)Case 2:[1][1][1][1][1][?][?][?][?][?] ==> 2^5 possibilities (2 x 2 x 2 x 2 x 2)[0][1][1][1][1][1][?][?][?][?] ==> 2^4 possibilities[?][0][1][1][1][1][1][?][?][?] ==> 2^4 possibilities[?][?][0][1][1][1][1][1][?][?] ==> 2^4 possibilities[?][?][?][0][1][1][1][1][1][?] ==> 2^4 possibilities[?][?][?][?][0][1][1][1][1][1] ==> 2^4 possibilities (1 possibility duplicated from case 1)Special Cases (don't count these, they are counted twice in previous cases)[0][0][0][0][0][1][1][1][1][1] ==> 1 possibility (counted in case 1)[1][1][1][1][1][0][0][0][0][0] ==> 1 possibility (counted in case 2)We need to subtract 2 from the final answer to account for this.As you can see, the number of possibilities for each case are:2^5 + 5(2^4) = 112There are two cases, you can multiply that by 2 to get your answer.2(2^5 + 4(2^4)) = 2(112) = 224 possibilitiesSubtract the special cases:224 possibilities - 2 possibilities = 222 possibilitiesThe answer to the question is:There are 222 unique ten bit strings that contain five consecutive zeros or five consecutive ones.
The vector representation of a convolutional code is g1=[1 1] and g2=[1 0]. If the received sequence is 11 11 01 10, we can use Viterbi Algorithm to decode it. The full trellis diagram, including the updated trellis state metrics, is shown below: Time t1: State 0 (00): Metric = 0 State 1 (10): Metric = 0 Time t2: State 0 (00): Metric = 0 + (1-1)^2 + (1-1)^2 = 0 State 1 (10): Metric = 0 + (1-1)^2 + (1-0)^2 = 1 Time t3: State 0 (00): Metric = 0 + (1-1)^2 + (1-1)^2 = 0 State 1 (10): Metric = 1 + (1-1)^2 + (1-0)^2 = 2 State 0 (01): Metric = 0 + (1-1)^2 + (0-1)^2 = 1 State 1 (11): Metric = 0 + (1-1)^2 + (0-0)^2 = 0 Time t4: State 0 (00): Metric = 0 + (1-1)^2 + (1-1)^2 = 0 State 1 (10): Metric = 2 + (1-1)^2 + (1-0)^2 = 3 State 0 (01): Metric = 1 + (1-1)^2 + (0-1)^2 = 2 State 1 (11): Metric = 0 + (1-1)^2 + (0-0)^2 = 0 Therefore, the decoded sequence is 11 11 01 10.
I was only able to get 13 but I think there can be more, this is what i got: 0+0+4=4 4+0+0=4 0+4+0=4 0+1+3=4 0+3+1=4 0+2+2=4 1+2+1=4 1+1+2=4 1+3+0=4 2+2+0=4 2+0+2=4 3+1+0=4 3+0+1=4
10 different combinations can be made. Raisins Peanuts Pretzels 3 0 0 2 1 1 2 0 1 1 2 0 1 0 2 1 1 1 0 0 3 0 3 0 0 1 2 0 2 1
Variance = sigma((value - mean)2) / (# values - 1) Mean = (0+1+1+2)/4 = 1 Variance = ((0-1)2+(1-1)2+(1-1)2+(2-1)2)/(4-1) Variance = (1+0+0+1)/3 Variance = 2/3 Variance ~ 0.667