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Logic Design التصميم المنطقي Second Course

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Syllabus Combinational Logic The NAND Gate as a Universal Logic Element. The NOR Gate as a Universal Logic Element. Bit Parallel Adder. Decoders. Encoders. Multiplexers. De-multiplexers Flip-Flop SR Flip-Flops. D Flip-Flops. JK Flip-Flops. Shift Register - Serial in \ Serial out shift Register Binary Counter - Asynchronous Binary Counter. - Synchronous Binary Counter. Syllabus Combinational Logic The NAND Gate as a Universal Logic Element. The NOR Gate as a Universal Logic Element. Bit Parallel Adder. Decoders. Encoders. Multiplexers. De-multiplexers Flip-Flop SR Flip-Flops. D Flip-Flops. JK Flip-Flops. Shift Register - Serial in \ Serial out shift Register Binary Counter - Asynchronous Binary Counter. - Synchronous Binary Counter. References 1-Computer System Architecture Third Edition M. Morris Mano 2- Digital Fundamentals Eight Edition FLOYD 3- Digital Fundamentals Ninth Edition FLOYD 4-Fundamentals of Digital Logic and Microcomputer Design Fifth edition M.RAFIQZZAMAN References 1-Computer System Architecture Third Edition M. Morris Mano 2- Digital Fundamentals Eight Edition FLOYD 3- Digital Fundamentals Ninth Edition FLOYD 4-Fundamentals of Digital Logic and Microcomputer Design Fifth edition M.RAFIQZZAMAN

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We have learned all the prerequisite material: – Truth tables and Boolean expressions describe functions – Expressions can be converted into hardware circuits – Boolean algebra and K-maps help simplify expressions and circuits Now, let us put all of these foundations to good use, to analyze and design some larger circuits Introduction

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Logic circuits for digital systems may be A combinational circuit consists of logic gates whose outputs at any time are determined by the current input values, i.e., it has no memory elements A sequential circuit consists of logic gates whose outputs at any time are determined by the current input values as well as the past input values, i.e., it has memory elements. Each input and output variable is a binary variable 2^n possible binary input combinations One possible binary value at the output for each input combination A truth table or m Boolean functions can be used to specify input-output relation

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A combinational circuit consists of : 1- Input variables. 2- Logic gates 3- Output variables Logic gates accepts signals ( Binary signals) from inputs and generate signals to the outputs.

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an example that converts binary coded decimal (BCD) to the excess-3 code for the decimal digits. The bit combinations assigned to the BCD and excess-3 codes are listed in Table. Since each code uses four bits to represent a decimal digit, there must be four input variables and four output variables.

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z = D y = CD + CD = CD + 1C + D2 x = BC + BD + BCD = B1C + D2 + BCD = B1C + D2 + B1C + D2 = B1C + D2 + B1C + D2 w = A + BC + BD = A + B1C + D2

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Half Adder this circuit needs two binary inputs and two binary outputs. The input variables designate the augend and addend bits; the output variables produce the sum and carry. We assign symbols x and y to the two inputs and S (for sum) and C (for carry) to the outputs. The truth table for the half adder is listed in Table. The C output is 1 only when both inputs are 1. The simplified Boolean functions for the two outputs can be obtained directly from the truth table. The simplified sum-of-products expressions are S = xy + xy C = xy

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The logic diagram of the half adder implemented in sum of products is shown in Fig. It can be also implemented with an exclusive-OR and an AND gate as shown in Fig. This form is used to show that two half adders can be used to construct a full adder.

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Full adder A full adder is a combinational circuit that forms the arithmetic sum of three bits. It consists of three inputs and two outputs. Two of the input variables, denoted by x and y, represent the two significant bits to be added. The third input, z, represents the carry from the previous lower significant position. Two outputs are necessary because the arithmetic sum of three binary digits ranges in value from 0 to 3, and binary representation of 2 or 3 needs two bits. The two outputs are designated by the symbols S for sum and C for carry. S = xyz + xyz + xyz + xyz C = xy + xz + yz

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