Computer Organization - signed bit number (2's complement and Magnitude)

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signed number in binary divided into 2 : [Video]

1.Signed Magnitude
2.Two complement

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1.Signed Magnitude

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Methode :

A10 = i=0Σn-2(2i*ai)  if an-1 = 0 A10 = -i=0Σn-2(2i*ai) if an-1 = 1

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Example:
0000 1010₂ = 10₁₀
1000 1010₂ = -10₁₀

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1.Two complement

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Methode :

A10 = i=0Σn-2(2i*ai)                   if A >= 0 A10 = -2n-1*an-1 + i=0Σn-2(2i*ai) if A  <  0

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Example:
0000 1010₂ = 10₁₀
1000 1010₂ = -2^7 + 10 = -128 + 10 = -118₁₀

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Example:

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1. Convert -20₁₀ in as Hexadecimal in form two's complement by 8bit size.

pow(2,7) + ? = -20
-128 + ? = -20
>>> -128.64.32.16.8.4.2.1
>>>  1.1.1.0.1.1.0.0
>>> -128+64+32+ 0+8+4+0+0 = 20
>>> 1110 1100 (Bin) = 0xEC ==>> -20 (Dec) = 0xEC

if from example 1 change size of bit to 10 then ==>> -20 (Dec) = 3EC₁₆
if 20bit ==>> -20₁₀ = FFFEC₁₆
if 22bit ==>> -20₁₀ = 3FFFEC₁₆

Totally : if number is negative then when increasing number of bit we just add the maximum of the most significant

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