[논리회로설계실험] 1bit full adder & 4bit full adder (logic gate 구현)(성균관대)

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1. Full Adder

Full adder는 가산기로 입력된 값의 합을 이진수로 표현하고 남는 값은 C를 통해 내보내는 기능을 한다. 1bit full adder에서는 A, B, Cin을 입력 받고 Sum으로 출력하며, Cin은 남는 값을 내보내는 역할을 한다. 4bit full adder는 1bit full adder를 모듈화하여 병렬로 4개 연결하고 새로운 A[n], B[n]의 값을 입력 받아 최종적인 값을 도출한다. 이를 통해 full adder는 모든 비트수에 대해 사용 가능하다는 것을 알 수 있다.
2. 1bit Full Adder 구현

1bit full adder의 경우 dataflow와 gatelevel로 구현하였다. dataflow 형식이 Boolean expression으로 표현하기에 직관적이고 한 눈에 보기 쉬웠다.
3. 4bit Full Adder 구현

4bit full adder는 gatelevel로 구현하였는데, 앞의 값에서 연속적으로 이어 진행하는 연산이다보니 비교적 gatelevel로 구현하는 것이 다른 형식에 비해 직관적이고 코드를 짜기에 알맞았다. 1bit full adder 모듈을 반복적으로 이용하여 구조를 가시적으로 파악할 수 있었고, 해당 모듈에서 발생한 오류를 한 눈에 찾기가 편리했다.

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1. Full Adder

A full adder is a digital circuit that performs the addition of three binary digits (bits) - the two bits being added and a carry bit from the previous less significant stage. It is an essential component in digital electronics and computer processors, as it forms the building block for larger arithmetic logic units (ALUs) and other complex arithmetic operations. The full adder takes two binary inputs (A and B) and a carry-in (Cin) from the previous less significant stage, and produces two outputs - the sum (S) and the carry-out (Cout) to the next more significant stage. The truth table and Boolean expressions for a full adder demonstrate its functionality in adding binary digits and propagating the carry. Full adders are widely used in various digital applications, from simple calculators to complex microprocessors, playing a crucial role in performing arithmetic operations efficiently and accurately.
2. 4bit Full Adder implementation

Implementing a 4-bit full adder is a more complex task compared to a 1-bit full adder, but it follows a similar approach. The key steps in implementing a 4-bit full adder include: 1. Constructing four 1-bit full adder modules, each responsible for adding the corresponding bits (A0-B0, A1-B1, A2-B2, A3-B3) and propagating the carry. 2. Connecting the carry-out of the least significant 1-bit full adder to the carry-in of the next more significant 1-bit full adder, creating a ripple carry structure. 3. Combining the sum outputs of the four 1-bit full adders to form the final 4-bit sum output. 4. Connecting the carry-out of the most significant 1-bit full adder as the carry-out of the entire 4-bit full adder. The implementation of a 4-bit full adder can be further optimized by using carry-look-ahead techniques, which reduce the propagation delay of the carry signal and improve the overall performance of the adder. The 4-bit full adder is a crucial component in larger arithmetic logic units (ALUs) and is widely used in digital systems, such as microprocessors, digital signal processors, and various other applications that require efficient and accurate arithmetic operations on multi-bit data. Understanding the design and implementation of a 4-bit full adder is essential for students and engineers working in the field of digital electronics and computer architecture.

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