2's Complement Circuit
نویسندگان
چکیده
This article introduces various Boolean operators which are used in discussing the properties and stability of a 2's complement circuit. We present the deenitions and related theorems for the following logical operators which include negative input/output: 'and2a', 'or2a', 'xor2a' and 'nand2a', 'nor2a', etc. We formalize the concept of a 2's complement circuit, deene the structures of comple-mentors/incrementors for binary operations, and prove the stability of the circuit. provide the notation and terminology for this paper. Let x be a set. Then hxi is a nite sequence with length 1. Let y be a set. Then hx; yi is a nite sequence with length 2. Let z be a set. Then hx; y; zi is a nite sequence with length 3. Let n, m be natural numbers, let p be a nite sequence with length n, and let q be a nite sequence with length m. Then p a q is a nite sequence with length n + m: Let S be an unsplit non void non empty many sorted signature, let A be a Boolean circuit of S, let s be a state of A, and let v be a vertex of S. Then s(v) is an element of Boolean. We now state two propositions: (1) For every function f and for all sets x 1 , x 2 such that x 1 2 dom f and x 2 2 dom f holds f hx 1 ; x 2 i = hf (x 1); f(x 2)i: (2) For every function f and for all sets x 1 , x 2 , x 3 such that x 1 2 dom f and x 2 2 dom f and x 3 2 dom f holds f hx 1 ; x 2 ; x 3 i = hf (x 1); f(x 2); f(x 3)i: The function and 2 from Boolean 2 into Boolean is deened by: (Def. 1) For all elements x, y of Boolean holds and 2 (hx; yi) = x ^ y: The function and 2a from Boolean 2 into Boolean is deened as follows: (Def. 2) For all elements x, y of Boolean holds (and 2a)(hx; yi) = :x ^ y: The function and 2b from Boolean 2 into Boolean is deened by: (Def. 3) For all elements x, y of Boolean holds (and 2b)(hx; yi) = :x ^ :y:
منابع مشابه
Białystok 2 ’ s Complement Circuit
This article introduces various Boolean operators which are used in discussing the properties and stability of a 2’s complement circuit. We present the definitions and related theorems for the following logical operators which include negative input/output: ’and2a’, ’or2a’, ’xor2a’ and ’nand2a’, ’nor2a’, etc. We formalize the concept of a 2’s complement circuit, define the structures of complem...
متن کامل2 ’ s Complement Circuit Katsumi Wasaki National College of Technology
This article introduces various Boolean operators which are used in discussing the properties and stability of a 2’s complement circuit. We present the definitions and related theorems for the following logical operators which include negative input/output: ’and2a’, ’or2a’, ’xor2a’ and ’nand2a’, ’nor2a’, etc. We formalize the concept of a 2’s complement circuit, define the structures of complem...
متن کاملDesign of a 4-bit 2’s Complement Reversible Circuit for Arithmetic Logic Unit Applications
Nowadays reversible circuit designing is the emerging area of research. This design strategy aims towards the formation of digital circuits with ideally zero power dissipation. In this paper we have proposed a new reversible logic module to design a 4-bit binary 2‟s complement circuit. This complement circuit using reversible logic can be used to design other low loss Arithmetic circuit. Propos...
متن کاملCMOS Based Design Simulation Of Adder /Subtractor Using Different Foundries
-In this paper a 4 bit parallel adder/subtractor circuit has been designed and analyzed. The circuit uses a controlled adder/subtractor circuit which converts the negative numbers into their 2’s complement. A comparative study of the silicon area and the power consumption has been done in the circuit using different channel lengths such as 65nm, 45nm. The circuit is designed and simulated using...
متن کاملA Novel Approach to Design 2-bit Binary Arithmetic Logic Unit (ALU) Circuit Using Optimized 8:1 Multiplexer with Reversible logic
Reversible circuit designing is the area where researchers are focussing more and more for the generation of low loss digital system designs. Researchers are using the concept of Reversible Logic in many areas such as Nanotechnology, low loss computing, optical computing, low power CMOS design etc. Here we have proposed a novel design approach for a 2-bit binary Arithmetic Logic Unit (ALU) usin...
متن کامل