Question

Please help me

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

Answer 1

The value of b is, 8

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 * 16^1)+(A * 16^0)=(6 * 16)+(10 * 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