Question

Assume 151 and 214 are unsigned 8-bit integers. Calculate 151 + 214 using saturating arithmetic. The result should be written in decimal. Show your work.

Short answer

The result of performing saturating arithmetic of 152+214 is as follows: 151+214 = 255 (365)

Step-by-step solution

Determine the addition operation

The binary values of the signed decimal numbers will be used for addition and subtraction. In addition, the rightmost bits will be added and the carry will be forwarded through the left. The operands should have values that fit 32 bits of specified bits.

Determine 151-214 using saturating arithmetic.

Given that, the 151 and 214 are signed 8-bit decimal integers. So, the range of the result must be between -128 to 127.

In saturation arithmetic, if the values are out of range fix them with maximum and minimum values.

So, now consider 151 to be the minimum range 128 and 214 to be the maximum range 127

Convert each of decimal numbers to binary:

128 = 10000000₂

127 = 01111111₂

Now add 128 and 127:

$$\begin{gathered} 128={10000000}_2 \\ 127={01111111}_2 \\ 128+127={11111111}_2 \end{gathered}$$

Now, convert 11111111 to decimal:

$$\begin{gathered} {11111111}_2=255 \\ 151+214=255\left(365\right) \end{gathered}$$

Therefore, the result of 151 and 214 saturate arithmetic addition is 255.