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marusya05 [52]
3 years ago
12

xpress the negative value -22 as a 2's complement integer, using eight bits. Repeat it for 16 bits and 32 bits. What does this i

llustrate with respect to the properties of sign extension as they pertain to 2's complement representation?  8 bit The 8-bit binary representation of 22 is 00010110. So, -22 in 2’s complement form is (NOT (00010110) + 1) = (11101001 + 1) = 11101010
Engineering
1 answer:
matrenka [14]3 years ago
4 0

Answer:

Explanation:

A negative binary number is represeneted by its 2's complement value. To get 2's complement, you just need to invert the bits and add 1 to it. So the formula is:

  twos_complement = ~val + 1

So you start out with 22 and you want to make it negative.

22₁₀ = ‭0001 0110‬₂    

~22₁₀ = ‭1110 1001‬₂   inverting the bits

~22₁₀ + 1 = ‭1110 1010‬₂   adding 1 to it.

so -22₁₀ == ~22₁₀ + 1 == ‭1110 1010‬₂

Do the same process for 16-bits and 32-bits and you'll find that the most significant bits will be padded with 1's.

-22₁₀ = ‭1110 1010‬₂     8-bits

-22₁₀ = ‭1111 1111 1110 1010‬‬₂     16-bits

-22₁₀ = ‭‭1111 1111 1111 1111 1111 1111 1110 1010‬‬‬₂  32-bits

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