Perform the following number conversions a Decimal number 12

Perform the following number conversions a) Decimal number 120 10 rightarrow binary Unsigned binary number 1001100 I_z electrical Decimal number -35 10 rightarrow 8 bit z\'s compliment number

Solution

Ans)

120₁₀=1*2⁶+1*2⁵+1*2⁴+1*2³+0*2²+0*2¹+0*2⁰

taking mantissa of exponents

120₁₀=1111000₂ (binary)

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

10011001₂=1*2⁷+0+0+1*2⁴+1*2³+0+0+1*2⁰=153₁₀ Decimal

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

-35₁₀

First we will binary equivalent of 35₁₀=1*2⁵+0+0+0+1*2¹+1*2⁰

35₁₀=100011₂

As we want 8bit answer append zeros

35₁₀=00100011₂-------1\'s compliment----11011100₂

   -----2\'s compliment=1\'s compliment+1=11011100₂+1=11011101₂

So -35₁₀=11011101₂