Question

Please help me Determine the value of base b if (152)b = 0x6A. Please show all steps.

Answer 1

Answer:

The value of b is, 8

Step-by-step explanation:

To determine the value of b:

Given:

$(152)_b = 0x6A$               ....[1]

Since, 0x6A represents the hexadecimal form.

To convert this hexadecimal form into decimal form:

$(6A)_{16}= (6 \times 16^1)+(A \times 16^0)=(6 \times 16)+(10 \times 1) =96+10 = 106$

⇒$0x6A=106$(decimal form)

Now we have to convert this decimal form into octal

8  |  106

8   |  13   | 2

    |   1    |  5

        1

Then, the octal form we get, $(152)_8$

Substitute this in [1] we have;

$(152)_b = (152)_8$

On comparing both sides we have;

b = 8

Therefore, the value of b is, 8