Question

Write the binary representation of the decimal number -64 (negative 64)

1. Assuming IEEE 754 single precision format
2. Assuming 8-bit 2’s complement representation
3. Assuming signed magnitude representation

Answer 1

(64)₁₀ =(1000000)₂

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(i) IEEE 754 single precision format:

Sign(S)(1bit)

Exponent(E)(8bits)

Mantissa(M)(23bits)

In Implicit form = (-1)^S * 1.M * 2^E-127

(-64)₁₀ = (-1)¹ * (1000000)₂

= (-1)¹ * (1.000000) *2⁶

= (-1)¹ * (1.000000) *2⁶⁺¹²⁷

= (-1)¹ * (1.000000) *2¹³³

Here, S=1, M=00000000, E= 133 = 10000101

(-64) in IEEE 754 single precision format =

1

10000101

00000000

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(ii)   8 bits 2's compliment representation:

(64)₁₀ =(01000000)₂

(-64)₁₀ in 8 bits 2's complement =(11000000)₂       ( ANSWER)

(-64)₁₀ in 16 bits 2's complement =(1111111111000000)₂

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(iii) Signed magnitude representation:

(-64)₁₀ in 8 bits signed magnitude representation =(11000000)₂

(-64)₁₀ in 16 bits signed magnitude representation =(1000000001000000)₂

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_{In 8 bits representation, both signed magnitude and 2's complement form looks same, but those two are different form if you see the 16 bits representation.}