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Digital Electronics : Combinational Circuits Part 1 ### COMBINATIONAL CIRCUITS

A logic circuit whose output depends directly on inputs and no other factor is known as combinational circuit. The most important types of combinational circuit are-- RAM, ROM, Multiplexers, Encoders, Decoders, Demultiplexers.

### MULTIPLEXERS

A multiplexer is a circuit with many inputs but only one output. A multiplexer has some data inputs, control inputs and one output. Depending on the control inputs, one input from the data inputs is sent to the output.

### DEMULTIPLEXERS

Demultiplex means 1 to many. A Demultiplexer is a circuit with one data input, few control inputs and many outputs. A Demultiplexer, depending on the control inputs, transfers the input to a desired output pin. The number of outputs is given by n as n ≤ 2m, where ‘m’ is the number of control inputs.

#### DECODER

A decoder is a logic circuit that converts a binary number to its equivalent decimal number. It is much like a Demultiplexer but it does not have any data input. A decoder circuit gives a 1(HIGH) at the output corresponding to the decimal equivalent of the input. For example—
if the inputs in the above figure are 010 then a 1(HIGH) will be observed at output ‘x2’. Similarly, if the input is 101, then a 1(HIGH) will be observed at output ‘x5’ and all other outputs will be 0(LOW).

### MEMORIES

The function of a memory is to store information. A memory is designed for bulk storage of data but that is all it can do. Some types of memories can remember the data even when the power is switched off.
The ability to remember data after the power is switched off is the dividing line between the two main types of memory. If it loses its data when the power is switched off, then we call the memory RAM or volatile memory. If it can hold on to the data without power, we call it ROM or non-volatile memory.

#### Different Kinds of ROM

A masked ROM is manufactured to our specification and cannot be changed. We must be very sure that the information is correct before it is made otherwise it all goes in the waste bin. The initial cost is necessarily high due to the expense of the tooling required.

#### Erasable programmable ROM (EPROM)

As the name suggests, this chip allows us to program it, then change our mind and try again. To erase the data there are two methods – ultraviolet light or electrical voltage pulses. EPROMs are ideal for prototyping since it is so easy to change the data to make modifications.

### The chip is bombarded with ultraviolet light via a transparent window on the chip. A specially constructed EPROM eraser provides the light. We pop the chip in, close the lid and switch on the timer. After a few minutes, the data is erased. When erased, all the data output is set to 1.

#### Electrically erasable programmable ROM (EEPROM)

This chip uses electrical voltage pulses as inputs to clear the previous data and is then reprogrammed in the same way as the UVEPROM.

We end this tutorial with a general introduction to RAM.

#### Introducing RAM

RAM (random access memory) accesses any memory location in the same amount of time regardless of where in the memory it happens to be stored. All memory, whether volatile or non-volatile is now designed as random access memory so it would be much better to divide the two types of memory into read/write and read only memory. Accessing memory - Each location in a memory is given a number, called an address. In the figure shown below, the 16 locations of memory would be numbered from 0 to 15, or in binary 0000–1111. The cells are formed into a rectangular layout, in this case a 4x4 square with four columns and four rows. To use a cell, the row containing the cell must be selected and the column containing the cell must also be activated. The shaded cell in figure has the address 0110 which means that it is in row 01 and in column 10. To access this cell we need to apply the binary address to the row and column decoders. When the address 0110 is applied, the first half of the address, 01, is applied to the row decoder and the second half of the address is applied to the column decoder. You will read more about RAM in the tutorial document below.

### Here's a list of all the tutorials we currently have in this area - Introductory Digital Electronic Circuits and Boolean logic

 Introduction to the Number System : Part 1 Introducing number systems. Representation of numbers in Decimal, Binary,Octal and Hexadecimal forms. Conversion from one form to the other. Number System : Part 2 Binary addition, subtraction and multiplication. Booth's multiplication algorithm. Unsigned and signed numbers. Introduction to Boolean Algebra : Part 1 Binary logic: True and false. Logical operators like OR, NOT, AND. Constructing truth tables. Basic postulates of Boolean Algebra. Logical addition, multiplication and complement rules. Principles of duality.  Basic theorems of boolean algebra: idempotence, involution, complementary, commutative, associative, distributive and absorption laws. Boolean Algebra : Part 2De-morgan's laws. Logic gates. 2 input and 3 input gates. XOR, XNOR gates. Universality of NAND and NOR gates. Realization of Boolean expressions using NAND and NOR. Replacing gates in a boolean circuit with NAND and NOR. Understanding Karnaugh Maps : Part 1 Introducing Karnaugh Maps. Min-terms and Max-terms. Canonical expressions. Sum of products and product of sums forms. Shorthand notations. Expanding expressions in SOP and POS Forms ( Sum of products and Product of sums ). Minimizing boolean expressions via Algebraic methods or map based reduction techniques. Pair, quad and octet in the context of Karnaugh Maps. Karnaugh Maps : Part 2Map rolling. Overlapping and redundant groups. Examples of reducing expressions via K-Map techniques. Introduction to Combinational Circuits : Part 1Combinational circuits: for which logic is entirely dependent of inputs and nothing else. Introduction to Multiplexers, De-multiplexers, encoders and decoders.Memories: RAM and ROM.  Different kinds of ROM - Masked ROM, programmable ROM. Combinational Circuits : Part 2 Static and Dynamic RAM, Memory organization. Introduction to Sequential Circuits : Part 1 Introduction to Sequential circuits. Different kinds of Flip Flops. RS, D, T, JK. Structure of flip flops. Switching example. Counters and Timers. Ripple and Synchronous Counters. Sequential Circuits : Part 2ADC or DAC Converters and conversion processes. Flash Converters, ramp generators. Successive approximation and quantization errors.