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**التصميم المنطقي Second Course**

Logic Design التصميم المنطقي Second Course

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**4-Fundamentals of Digital Logic and**

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 4-Fundamentals of Digital Logic and Microcomputer Design Fifth edition M.RAFIQZZAMAN

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**Introduction • 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

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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 mustbe 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 w = A + BC + BD = A + B1C + D2

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**S = xy + xy C = xy 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 S = xyz + xyz + xyz + xyz C = xy + xz + yz**

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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