Two's complement in the context of "16 bit"

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⭐ Core Definition: Two's complement

Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. As with the ones' complement and sign-magnitude systems, two's complement uses the most significant bit as the sign to indicate positive (0) or negative (1) numbers, and nonnegative numbers are given their unsigned representation (6 is 0110, zero is 0000); however, in two's complement, negative numbers are represented by taking the bit complement of their magnitude and then adding one (−6 is 1010). The number of bits in the representation may be increased by padding all additional high bits of negative or positive numbers with 1's or 0's, respectively, or decreased by removing additional leading 1's or 0's.

Unlike the ones' complement scheme, the two's complement scheme has only one representation for zero, with room for one extra negative number (the range of a 4-bit number is −8 to +7). Furthermore, the same arithmetic implementations can be used on signed as well as unsigned integersand differ only in the integer overflow situations, since the sum of representations of a positive number and its negative is 0 (with the carry bit set).

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👉 Two's complement in the context of 16 bit

In computer architecture, 16-bit integers, memory addresses, or other data units are those that are 16 bits (2 octets) wide. Also, 16-bit central processing unit (CPU) and arithmetic logic unit (ALU) architectures are those that are based on registers, address buses, or data buses of that size. 16-bit microcomputers are microcomputers that use 16-bit microprocessors.

A 16-bit register can store 2 different values. The range of integer values that can be stored in 16 bits depends on the integer representation used. With the two most common representations, the range is 0 through 65,535 (2 − 1) for representation as an (unsigned) binary number, and −32,768 (−1 × 2) through 32,767 (2 − 1) for representation as two's complement. Since 2 is 65,536, a processor with 16-bit memory addresses can directly access 64 KiB (65,536 bytes) of byte-addressable memory. If a system uses segmentation with 16-bit segment offsets, more can be accessed.

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Two's complement in the context of Analog-to-digital converter

In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as from fingers touching a touchscreen, sound entering a microphone, or light entering a digital camera, into a digital signal.

An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.

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Two's complement in the context of Half adder

An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors, adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators and similar operations.

Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers.In cases where two's complement or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor.Other signed number representations require more logic around the basic adder.

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LINKED FROM (PARENTS)
← Analog-to-digital converter ← 16 bit ← Analog-to-digital conversion ← 16-bit processor ← 16-bit ← Half adder ← Full adder
LINKS TO (CHILDREN)
Signed number representations → Integer (computer science) → Fixed-point arithmetic → Ones' complement → Sign-magnitude → Most significant bit → Bit complement →