Question

Find out the value of X y and z in the following (A2F.8)16=(X)8=(Y)10=(z)2

Answer 1

Answer:

Explanation:

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Answer 2

Answer:

According to our calculations,

The value of x = 5057.4

The value of y = 2607.5

The value of z = 101000101111.1

Explanation:

• Hexadecimal is base-16 in the numeric system, and octal is base-8. We can actually do this by performing the following steps:

• To accomplish this, change the hexadecimal number to decimal first, and then the resultant decimal to octal.

• Starting with one, multiply the one's location in hexadecimal by $16^0$, the tens place by $16^1$, the hundreds place by $16^2$, and so on from right to left.

• To find the decimal equivalent of a particular hexadecimal value, add all the products we obtained in step 1.

• Divide the decimal value obtained in step 2 by 8 while paying attention to the quotient and the remainder.

• Once you reach a quotient of zero, keep dividing the quotient by 8 as before.

• To get the octal equivalent of a decimal number, simply put the remainders in reverse order.

• First, use the formulas above to convert $A2F.8_1_6$ to decimal form:

= $A2F_1_6$

= Ax $16^2$ + 2 x $16^1$ + F x $16^0$ + 8 x $16^_^1$

= $2607.5_1_0$

Now, we have to convert it to octal

2607 / 8 = 325 and with remainder 7

325 / 8 = 40 and Iwith remainder 5

40 / 8 = 5 with remainder 0

5 / 8 = 0 with remainder 5

2607 = 5057 -------(1)

Follow these procedures to convert the decimal fraction 0.5 to an octal number:

• Take note of the resulting integer and fractional parts when you multiply 0.5 by 8 while doing so.
• Once the resulting fractional component is equal to zero, keep multiplying by 8 until you reach that point (we calcuclate upto ten digits).
• Then, to obtain an identical octal number, simply write out the integer components from each multiplication result.

0.5 × 8 = 4 + 0

0.5 = 0.4 ------- (2)

$2607.5_1_0 = 5057.4_8$

Therefore, hexadecimal number A2F.8 converted to octal is equals: 5057.4 which is the value of x

Similarly for y :

• The hexadecimal number A2F.8 is converted to its equivalent decimal number by first converting its integral and fractional parts separately.

First decimal equivalent of "F" = (F) 15 × $16^0$= 15

Then decimal equivalent of "2" = 2 × $16^1$= 32

Now, decimal equivalent of "A" = (A) 10 × $16^2$ = 2560

And decimal equivalent of "A2F" = 25603215

A2F = 2607

Similarly decimal equivalent of "8" = 8 × $16^-^1$ = 0.5

Hence, decimal equivalent of "0.8" = 0.5

0.8 = 0.5

Here is the conclusion: Therefore, the decimal representation of the hexadecimal number A2F.8 is: $=2607_1_0+0.5_1_0 = 2607.5_1_0$

Therefore value of y is 2607.5

Now for z :

firstly, compute $A2F.8_1_6$ in decimal form -

= $A2F_1_6$

= A × $16^2$ + 2 × $16^1$ + F × 1608 × $16^-^1$

= $2607.5_1_0$

We must now translate 2607.510 into binary.

2607 / 2 = 1303 (remainder 1)

1303 / 2 = 651 (remainder 1)

651 / 2 = 325 (remainder 1)

325 / 2 = 162 (remainder 1)

162 / 2 = 81 (remainder 0)

81 / 2 = 40 (remainder 1)

40 / 2 = 20 (remainder 0)

20 / 2 = 10 (remainder 0)

10 / 2 = 5 (remainder 0)

5 / 2 = 2 (remainder 1)

2 / 2 = 1 (remainder 0)

1 / 2 = 0 (remainder 1)

2607 = 101000101111 ------- (1)

0.5 converted from a decimal to a binary number :

0.5 × 2 = 1 + 0

0.5 = 0.1 ------- (2)

2607.5$_1_0$ = 101000101111.1$_2$

The binary equivalent of the hexadecimal number A2F.8 is thus: 101000101111.1 is the value of z.

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