Question

Assume 151 and 214 are signed 8-bit decimal integers stored in two’s complement format. Calculate 151 + 214 using saturating arithmetic. The result should be written in decimal. Show your work

Answer 1

Answer:

-128

Explanation:

$(151)_{10}$

We have to convert this decimal number into the binary number

$(10010111) _{2}$

Performing the 2's complement number so we have to subtract 1 from this

$10010111 -1 \\=(10010110)_{2}$

Now to getting the original number we have to complement the previous number it means convert 1 ->0 and 0 -> 1

$(10010110)_{2} ---->(01101001)_{2}$

The previous number is converted binary to decimal we get ,

$(01101001)_{2}=(105) _{10}$

-105(According to the rule of 2's complement )

Similarly same process will apply on the $(214)_{10}$

We have to convert this decimal number into the binary number

$(11010110)_{2}$

Performing the 2's complement number so we have to subtract 1 from this

$11010110 - 1 =(11010101)_{2}$

Now to getting the original number we have to complement the previous number it means convert 1 ->0 and 0 -> 1

$(11010101)_{2}---------> (00100101)_{2}$

The previous number is converted binary to decimal we get ,

$(00100101)_{2}------->(42)_{10}$

-42(According to the rule of 2's complement )

Therefore the result is

151 + 214

=(-105 + (-42)

=-147

Hence the -147 is smaller then -128 that is smaller 8 bit signed integer is Therefore result is : -128