Answer to Question #119451 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

110101.0110₂ in Octal:

integer part:             110101₂ = 110 101₂ = 65₈

fractional part:          0110₂ = 011 000₂ = 50₈

Result: 110101.0110₂ = 65. 50₈

 

10110.1010₂ in Octal:

integer part:             10110₂ = 010 110₂ = 26₈

fractional part            1010₂ = 101 000₂ = 50₈

Result: 10110.1010₂ = 26. 50₈

 

Compute in octal number system:

  65. 50₈

- 26. 50₈ 

= 36.60₈

 

Result: 36.60₈

 

 

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

15's complement of E5ACF₁₆:

  FFFFFF₁₆

– E5ACF₁₆

= 1A530₁₆

 

 Add this 15's complement to E7BAD₁₆:

    E7BAD₁₆ 

+  1A530₁₆

= 1020DD₁₆

 

1020DD₁₆

    +   1(cary)

= 20DE₁₆

 

Result: 20DE₁₆

 

 

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

2's complement of -45₁₀ is:

 1 010011₂ (Invert 0 and 1 of a given binary number. Then add 1.)

 

Add 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