# Theory of Logic Circuits

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## Addition using sign magnitude representation

• Politechnika Śląska
• Theory of Logic Circuits
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Addition using sign magnitude representation In the case of sign magnitude representation addition is a little complicated. The addition algorithm contains several steps: 1. Check signs of both numbers. 2. If signs are equal (both are positive or negative) add magnitudes and use the sign as sign...

## Algorithm description

• Politechnika Śląska
• Theory of Logic Circuits
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Algorithm description Kazakow algorithm is efficient, small and fast way, providing irredundant solution for output function, given by many input signals (i.e. 20 and more), when output is weakly specified function. Weakly specified function is the one that is given by a small amount of one's com...

## Asynchronous counters

• Politechnika Śląska
• Theory of Logic Circuits
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Asynchronous counters In asynchronous counters the control inputs of flip-flops are not driven by the same signal source. The common element used in a design of such a counter is a simplified symbol of a flip-flop. By such symbol we understand any flip-flop working as a frequency divider by 2. I...

## Asynchronous sequential logic circuits

• Politechnika Śląska
• Theory of Logic Circuits
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Asynchronous sequential logic circuits All switching circuits belong to one of two classes: combinational or sequential. On contrary to combinational logic circuits, the operation of sequential ones is dependent not only on the present state of external inputs, but also on the state of these inpu...

• Politechnika Śląska
• Theory of Logic Circuits
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Bi nary adders Binary adder is a basic circuit performing addition operation for binary numbers A and B. This simple combinational circuit obtains two signals Si (sum) and Ci+1 (carry to next position) from signals Ai, Bi and Ci (carry from previous position). Fig. 1 presents the truth table and ...

## Metoda Huffmansa

• Politechnika Śląska
• Theory of Logic Circuits
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Huffman's Method 1. Obtain the primitive flow map of the circuit 2. Reduce equivalent and pseudo-equivalent states and obtain the primitive flow map without redundant states 3. Merge rows of the primitive flow map without redundant states (The m...

## Basics

• Politechnika Śląska
• Theory of Logic Circuits
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Basics Basic idea when using Table of Switching Sequence method is to follow four main steps: - preparing description of working system, means to formulate conditions of working, - preparing and description presentation of working system by the method Table of Successive Connection, - hacking s...

## Binary comparators

• Politechnika Śląska
• Theory of Logic Circuits
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Binary comparators Another type of logic circuit used with binary numbers is a comparator. Fig. 3 presents the logic symbol and the truth table of 1-bit comparator. This circuit sets exactly one of outputs “AB” into state 1 according to compared digits Ai and Bi and input signals “”. Like adder...

## Arithmetic operations

• Politechnika Śląska
• Theory of Logic Circuits
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Arithmetic operations The operations of addition, subtraction, multiplication, and division can be carried out in exactly the same manner with binary numbers as they are with decimal numbers. When number is in 1's or 2's complement representation, computer needs to use only Adder circuit and Com...

## Asynchronous flipflops

• Politechnika Śląska
• Theory of Logic Circuits
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Asynchronous flip-flops In practice only sr flip-flops (and their modifications, like: ~s~r flip-flops) are built as asynchronous devices1. First let us consider sr basic latch implemented with the use of two NOR gates The logical symbol of this bistable device is given in the Fig.2. Numbers asso...