# Digital Design

## Logical Equivalence – Domination Laws

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13 total views In the previous article, you learnt about Identity law which is an equivalence. Similarly, the domination law are another equivalence that you are going to learn in this article. Also, this equivalence need proof which is the main purpose of this document. The prove is in the form of truth table for domination …

## Simplifying Boolean Function using K-Map -Special Case

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110 total views K-Map technique is a straight forward and simple method for minimizing Boolean functions. In this article, you will learn a special case of K-map, when the function is in a Standard Sum of Product and not in a Canonical Sum of Product form. For example In function1, each term is called a minterm( …

## Subtraction using 10’s complement

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162 total views In digital computer systems, arithmetic operations are simplified using the radix complement system also known as r’s complement system. The r stands for radix which is a base for a number in a particular number system. In this post, you learn to do subtraction using 10’s complement. You must be familiar with the …

## Sequential Circuits – Flip Flop Circuits

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19 total views Sequential Circuits have a memory element in addition to a combinational circuit so it remembers one bit of information. If a sequential circuit uses a clock pulse, then it is called “Clocked Sequential Circuit”. There are two types of Sequential Circuits, Synchronous Sequential Circuits Asynchronous Sequential Circuits In synchronous sequential circuits the memory …

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43 total views The adder is a combinational circuit that add binary digits for arithmetic computation. A combinational circuit is a kind of digital circuit that has an input, a logic circuit and an output. For n variables, there are 2n combinations of input variables and for each input combination, there is one and only one …

## Combinational Circuit – Questions/Solutions

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62 total views In this post, you will learn example problems from combinational circuits. These problems help in minimizing Boolean functions and constructing logic circuit diagrams. The solution to the problems are given in step-by-step manner with explanation wherever possible. Q1. Simplify the Boolean function using K-MAP technique. F(A,B,C,D) = Σ( 0,1,4,8,9,10 ); Solution:There are 4 …

## Understanding Sum of Minterms and Product of Maxterms

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793 total views A Boolean function is expressed in two form. Sum of Minterms Product of Maxterms Sum of Minterms x’ y’ z , x y’ z’ , x y’ z  , x y z’  , x y z   , gives 1 as output in the above Truth Table. Literal –  x, y, A, b …

## Universal Gates

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50 total views In computer science, logic gates such as NAND gates are very useful. You can use NAND gate as universal gate. They can be helpful in designing any complex logic circuit its implementation using NAND gates only. In this post you learn to use NAND as universal gate to create a logic diagram of …

## Subtraction of signed binary numbers using 2’s Complement

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41 total views In this article, we will perform a subtraction using 2’s complement. An unsigned binary number does not have a sign bit in the most significant bit (MSB) position. For example, consider 8-bit representation of 3810 3810 = 01001002 = 0. 27 + 0. 26 + 1. 25 + 0. 24 + 0. 23 …

## 4-Variable K-Map

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143 total views Previous post, you learned about 3-variable K-map, and learned how to minimize a boolean function. In this post, you will learn about bigger map such as a 4-variable K-map. With 4-variable map you will be able to make larger groups of cells. Plotting a 4-variable K-map The 4 variables of a boolean function …