Question

Find the Hamming weight of

(a)$\mathbf{0110110}\mathbf{\in }\mathit{B}\left(7\right)$

(b)$\mathbf{11110011}\mathbf{\in }\mathit{B}\left(8\right)$

(c)$\mathbf{000001}\mathbf{\in }\mathit{B}\left(6\right)$

(d)$\mathbf{101101101101}\mathbf{\in }\mathit{B}\left(12\right)$

Short answer

1. The humming weight $\text{Wt}\left(0110110\right)=4$.
2. The humming weight$\text{Wt}\left(11110011\right)=6$ .
3. The humming weight$\text{Wt}\left(000001\right)=1$.
4. The humming weight $Wt\left(101101101101\right)=8$.

Step-by-step solution

Definition of humming weight

The Hamming weight of an element u of $B\left(n\right)$.Is the number of nonzero

coordinates in u; it is denoted $Wt\left(u\right)$.

(a)Step 2: Finding the humming weight 

Given in the question,

$0110110\in B\left(7\right)$

So,$u=0110110$

The number of nonzero elements in u is 4.

Therefore, according to the definition of humming weight, the humming weight .

$\text{Wt}\left(0110110\right)=4$

(b)Step 3: Finding the humming weight 

Given in the question,

$11110011\in B\left(8\right)$

So, $u=11110011$

The number of nonzero elements in u is 6.

Therefore, according to the definition of humming weight, the humming weight .

$\text{Wt}\left(11110011\right)=6$

(c)Step 4: Finding the humming weight

Given in the question,

$000001\in B\left(6\right)$

So, $u=000001$

The number of nonzero elements in u is 1.

Therefore, according to the definition of humming weight, the humming weight .

$\text{Wt}\left(000001\right)=1$

(d)Step 5: Finding the humming weight

Given in the question,

$101101101101\in B\left(12\right)$

So, $u=101101101101$

The number of nonzero elements in u is 8.

Therefore, according to the definition of humming weight, the humming weight .

$\text{Wt}\left(101101101101\right)=8$