An embedded flight-control system uses 8-bit two's complement representation to store velocity adjustments, giving a representable range of -128 to +127. During a corrective maneuver, the system attempts to add two positive adjustments represented in binary as 010010112 01001011_2\,010010112 and 01010110201010110_2010101102.
Which of the following statements correctly describes the outcome of this addition and the nature of the error that occurs?
The calculation completes successfully with a result of 10100001210100001_2101000012 (16110161_{10}16110), because two's complement automatically extends the register length by 1 bit to accommodate positive values up to 255255255.
An overflow error occurs because the sum (16110161_{10}16110) exceeds the maximum representable positive value (+127+127+127). The sign bit becomes 111, incorrectly representing the value as −9510-95_{10}−9510.
An underflow error occurs because the addition of two positive values results in a carry-out from the most significant bit, dropping the value below −128-128−128.
An overflow error occurs because a carry-out of 111 from the most significant bit is generated into the ninth bit, but since the sign bit remains 000, the result is interpreted as a positive 331033_{10}3310.
Practise Edexcel GCSE Computer Science Binary with exam-style questions for GCSE Computer Science. 100 questions covering Binary representation and number of states, Unsigned and two's complement integers, Converting denary and 8-bit binary, Binary addition and binary shifts, Concept of overflow, and Hexadecimal notation and conversion, matched to the Edexcel GCSE Computer Science (1CP2) specification and written in Paper 1 and Paper 2 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.