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

In two's complement format with saturating arithmetic, the sum of 151 and 214, which are both outside the 8-bit signed integer range, would saturate at the maximum value of 127.

Step-by-step explanation:

The question is about calculating the sum of two signed 8-bit decimal integers, 151 and 214, using two's complement format and saturating arithmetic. In an 8-bit signed integer representation, the largest positive integer is 127. Adding 151 and 214 exceeds this range; thus, in saturating arithmetic, the sum would saturate at the maximum value, which is 127 in this case. Therefore, the result of 151 + 214 in saturating arithmetic is 127.

Answer 2

-128

Step-by-step 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