Hey all please I need help with this question and for 2c ple

Hey all please I need help with this question, and for 2c please I need a good excplantion.

Thank you in advance!

  2a. Convert unsigned binary 1101 1010 0001 1010 to decimal.

2b. Convert 16-bit two’s complement binary 1101 1010 0001 1010 to decimal.

2c. Do the results of #2a and #2b have the same decimal value? Why or why not?

Solution

2a.

Unsigned binary number is 1101 1010 0001 1010.

1101 1010 0001 1010

= 1*2¹⁵ + 1*2¹⁴ + 1*2¹² + 1*2¹¹ + 1*2⁹ + 1*2⁴ + 1*2³ + 1*2¹

= 55834

Threfore 1101 1010 0001 1010 = 55834.

2b.

16-bit two’s complement binary number is 1101 1010 0001 1010.

Find 1\'s complement of the number.

Find 2\'s complement of the number.

0010 0101 1110 0101

1

..............................................................................

0010 0101 1110 0110

The original binary number is 0010 0101 1110 0110.

Convert binary to decimal number :

The value of 0010 0101 1110 0110 is

= 1*2¹³ + 1*2¹⁰ + 1*2⁸ + 1*2⁷ + 1*2⁶ + 1*2⁵ + 1*2² + 1*2¹

= 9702

Therefore the decimal value of 16-bit two’s complement binary is 9702.

2c.

Answer is NO.

Reason :

The decimal value of 2a is 55834.

The decimal value of 2b is 9702.

Since 55834 is not equal to 9702, #2a and #2b have no same decimal value.