Answer to Question #119556 in Algorithms for desmond

Question

7.Compute 110101.01102-10110.10102 in octal number system.
8.Compute the value of E7BAD16-E5ACF16 in 15’s complement and write your final answer in binary.
9.Compute the value of 5510-4510 using 7-bit 2’s complement sign magnitude number

Answer 1

Compute 110101.0110₂-10110.1010₂ in octal number system

 

Conversion  110101.0110₂ in Octal:

Divide the source code of the integer part of the number into groups of 3 digits:

110101₂ = 110 101₂

Then replace each group with binary code:

110 101₂  = 65₈

 

Conversion the fractional part of the number. To do this, divide the source code into groups of 3 digits:

0110₂ = 011 000₂ = 50₈

Result: 110101.0110₂ = 65. 50₈

 

Conversion  10110.1010₂ in Octal:

Divide the source code of the integer part of the number into groups of 3 digits:

10110₂ = 010 110₂

Then replace each group with binary code:

010 110₂ = 26₈

 

Conversion the fractional part of the number. To do this, divide the source code into groups of 3 digits:

1010₂ = 101 000₂ = 50₈

Result: 10110.1010₂ = 26. 50₈

 

  65. 50₈

- 26. 50₈ 

  36.60₈

Answer: 36.60₈

 

 

 

Compute the value of E7BAD₁₆-E5ACF₁₆ in 15’s complement and write your final answer in binary.

 

Compute in Hex:

 E7BAD₁₆

-E5ACF₁₆

  20DE₁₆

 

Compute using 15's complement.

1)     15's complement of a number is obtained by subtracting all bits from FFFFF₁₆:

15's complement of E5ACF₁₆ is:

FFFFFF₁₆ – E5ACF₁₆ =  1A530₁₆

  FFFFFF₁₆

– E5ACF₁₆

  1A530₁₆

 

2)     Now Add this 15's complement

    E7BAD₁₆ 

+  1A530₁₆

  1020DD₁₆

---------------------

1020DD₁₆     

    + 1 (cary)

= 20DE₁₆

 

Answer: 20DE₁₆

 

 

 

Compute the value of 55₁₀-45₁₀ using 7-bit 2’s complement sign magnitude number.

 

Compute  in Dec:

55₁₀ - 45₁₀ = 10₁₀

 

Compute  in Bin:

 110111₂ 

- 101101₂

=    1010₂

 

Compute using 7-bit 2’s complement sign magnitude number:

2's complement of -45 is: 1 010011₂ (Invert 0 and 1 of a given binary number. Then add 1.)

 

Add this 2's complement of  45₁₀ to 55₁₀

0 110111₂               (55₁₀)

+

1 010011₂              (2’s complement 45₁₀)

---------------------------------------------

 0001010₂

end-around-carry-bit addition does not occur in 2's complement arithmetic operations. It is ignored.

 

Answer: 0001010₂