What is the result if you add two decimal numbers (45+216), expressed in binary using 8-bit unsigned precision?

261

Explanation:

Adding up two decimal numbers ( 45 + 216 ) expressed in binary using 8-bit unsigned precision

first we express the decimal numbers in 8-bit unsigned precision :

45 = 32 + 8 + 4 + 1 = 2^5 + 2^3 + 2^2 + 2^0 = 00101101

216 = 2^7 + 2^6 + 2^4 + 2^3 = 11011000

Adding the numbers together =  00101101

                                                   + 11011000

                                                 = 100000101 = 261 ( an overflow occurred )

note : The maximum value that can be expressed with 8-bit unsigned precision is  = 2^8 - 1 = 256

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