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Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...
Using sign-magnitude representation requires only complementing the sign bit of the subtrahend and adding, but the addition/subtraction logic needs to compare the sign bits, complement one of the inputs if they are different, implement an end-around carry, and complement the result if there was no carry from the most significant bit.
There are tricks for implementing packed BCD and zoned decimal add–or–subtract operations using short but difficult to understand sequences of word-parallel logic and binary arithmetic operations. [49] For example, the following code (written in C) computes an unsigned 8-digit packed BCD addition using 32-bit binary operations:
Mainframes such as the IBM System/360, the GE-600 series, [2] and the PDP-6 and PDP-10 use two's complement, as did minicomputers such as the PDP-5 and PDP-8 and the PDP-11 and VAX machines. The architects of the early integrated-circuit-based CPUs (Intel 8080, etc.) also chose to use two's complement math.
Adding BCD numbers using these opcodes is a complex task, and requires many instructions to add even modest numbers. It can also require a large amount of memory. [ 2 ] If only doing integer calculations, then all integer calculations are exact, so the radix of the number representation is not important for accuracy.
In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. [1] [2] It is also known as the shift-and-add-3 algorithm, and can be implemented using a small number of gates in computer hardware, but at the expense of high latency. [3]
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