Question

The square of the binary number 1001 in hexadecimal is      

  a. 81    b. 51    c. 121    d. A1

Answer 1

it will be 9^2=81

hexadecimal of (81)₁₀=(51)₁₆

Answer 2

given:

binary number =1001

The square of the binary number (1001) = 1010001

To convert from binary to hexadecimal (1010001=0101 | 0001)

0101=5 and 0001=1 so answer=51 option (B)

Answer 3

Another approach  finding the square of the binary

position	4	3	2	1
bit	1	0	0	1

Here, we have to find the position of 1 in the given binary number

In this example, the position of 1 are 1 and 4

append zeros equal to the $position (1) - 1$ to the right and add all the values to get the desired result

$1 - 1 = 0$ ( 0 zeros to be appended)

$4 - 1 = 3$ ( 3 zeros to be appended)

$1001_{2}+ 1001000_{2} = 1010001_{2} = 51_{16}$

Example 2:

suppose, you want to square $101100$.

the position of $1$ are $3, 4$ and $6$

$ ( 3 - 1 ) = 2 $ $\Rightarrow$$10110000_{2}$

$( 4 - 1 ) = 3$  $\Rightarrow$$101100000_{2}$

$(6-1 ) = 5$ $\Rightarrow$$10110000000_{2}$  

$10110000_{2} + 101100000_{2} + 10110000000_{2} = 11110010000_{2}$