GO Classes DPP | GATE CS | Digital Logic | Base Arithmetic

Answer 1

To solve the base $8$ (octal) subtraction problem:

$$(6251)_8 - (3x74)_8 = (2555)_8$$

We can rearrange the equation to solve for the unknown term $(3x74)_8$:

$$(3x74)_8 = (6251)_8 - (2555)_8$$

 

Now, we will perform the subtraction column by column (from right to left) in base $8$. 

Remember that when borrowing, we borrow $8$ (the base) rather than $10$.

 

To find $x$, we compute $(6251)_8 - (2555)_8$ in base $8$:

$$\begin{array}{r@{\quad}l} (6251)_8 \\ - (2555)_8 \\ \hline \end{array}$$

Step-by-step calculation:

• Units place: $1 - 5$. We cannot do this, so we borrow $1$ from the $8^1$ column.

  • New value: $(1 + 8) - 5 = 4$.

• $\mathbf{8^1}$ place: The $5$ in the original $6251$ became $4$ after the borrow. Now we have $4 - 5$. We cannot do this, so we borrow $1$ from the $8^2$ column.

  • New value: $(4 + 8) - 5 = 7$.

• $\mathbf{8^2}$ place: The $2$ in the original $6251$ became $1$ after the borrow. Now we have $1 - 5$. We cannot do this, so we borrow $1$ from the $8^3$ column.

  • New value: $(1 + 8) - 5 = 4$.

• $\mathbf{8^3}$ place: The $6$ in the original $6251$ became $5$ after the borrow.

  • New value: $5 - 2 = 3$.

• Putting it all together, the result is:

  $$\begin{array}{r@{\quad}l} (6251)_8 \\ - (2555)_8 \\ \hline (3474)_8 \end{array}$$

• Comparing this to the term $(3x74)_8$, we find that:

  $$\boxed{x = 4}$$

Comments

Note : When in exam if you encounter a problem like this with a variable in the middle of a subtrahend or minuend, rearranging the equation is the safest method. Doing the subtraction "in place" with the unknown variable $x$ creates a high risk of making a "borrowing" error. By moving the term to the other side, you convert an algebra problem into a simple, deterministic arithmetic problem, which is much faster to verify.

Answer 2

X=4 is the answer

Answer 3

Here is the explanation