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BINARY CODED DECIMAL (BCD)

By Dinesh Thakur

The binary coded decimal (BCD) is a type of binary code used to represent a given decimal number in an equivalent binary form. Its main advantage is that it allows easy conversion to decimal digits for printing or display and faster calculations.

The most common BCD code is the 8421 BCD code. In this, the BCD equivalent of a decimal number is written by replacing each decimal digit in integer and fractional parts with its four-bit binary equivalent ‘(or nibble). Here 8, 4, 2 and 1 represent the weights of different bits in the four-bit groups, starting from the (MSB) most significant bit (to extreme left) and proceeding towards the least significant (LSB) bit.

This feature makes it a weighted code, whose main characteristic is that each binary digit in the four bit group representing a given decimal digit is assigned a weight, and for each group of four bits, the sum of the weights of those binary digits whose value is 1 is equal to the decimal digit which they represent.

For example, if we look at table, we find that the decimal digit 9 when represented in 8421 BCD is 1001. Now the decimal digit assigned to first 1 is 8 and to the second 1 is 1. If we add 8 and 1 we get the required decimal number which is 9.

 BCD Code Chart

The 4221 BCD and 5421 BCD are other weighted BCD codes shown in table. The numbers 4, 2, 2, 1 in 4221 BCD and 5, 4, 2 and 1 in 5421 BCD represent weights of the relevant bits.

Now let us consider some examples, where we convert the given decimal numbers to BCD.

The 8421 BCD code for 9.2 is 1001.0010.

 BCD for 9.2

The 4221 BCD code for 9.2 is 1111.0010.

The 5421 BCD code for 9.2 is 1100.0010.

BCD code is useful for outputting to displays that are always numeric (0 to 9), such as those found in digital clocks or digital voltmeters.

Classification of Various Binary Code

By Dinesh Thakur

Digital data is represented, stored and transmitted as groups of binary digits also known as binary code. The binary codes can be classified as shown in Fig.

Classification of various binary code

Weighted codes: In weighted codes, each digit is assigned a specific weight according to its position. For example, in 8421BCD code, 1001 the weights of 1, 0, 0, 1 (from left to right) are 8, 4, 2 and 1 respectively.

Suppose W1‘ W2‘ W3 and W4 are the weights of binary digits and Xl‘ X2, X3 and X4 are the corresponding digit values then decimal digit. N = W1 Xl + W2 X2 + W3 X3 + W4 X4 is represented by binary sequence X4 X3 X2 X4.

The codes 8421BCD, 2421BCD, 5211BCD are all weighted codes.

• Non-weighted codes: The non-weighted codes are not positionally weighted. In other words, each digit position within the number is not assigned a fixed value ( or weight ).

             Excess-3 and gray code are non-weighted codes.

• Reflective codes: A code is reflective when the code is self complementing. In other words, when the code for 9 is the complement the code for 0, 8 for 1, 7 for 2, 6 for 3 and 5 for 4.

             2421BCD, 5421BCD and Excess-3 code are reflective codes.

• Sequential codes: In sequential codes, each succeeding ‘code is one binary number greater than its preceding code. This property helps in manipulation of data.

             8421 BCD and Excess-3 are sequential codes.

• Alphanumeric codes: Codes used to represent numbers, alphabetic characters, symbols and various instructions necessary for conveying intelligible information.

             ASCII, EBCDIC, UNICODE are the most-commonly used alphanumeric codes.

• Error defecting and correcting codes: Codes which allow error defection and correction are called error detecting and’ correcting codes. Hamming code is the mostly commonly used error detecting and correcting code.

Digital System

By Dinesh Thakur

In digital circuit, a signal is represented in discrete states or logic levels. Digital signals are non-continuous and change in individual steps. They consist of pulses with discrete levels. The value of each pulse is constant but there is an abrupt change from one digit to next.

The signals in all present-day electronic digital systems have only two discrete values and are said to be binary. The digital-system design is restricted to use binary signals because of lower reliability of many valued electronic circuits. A circuit with ten states, using one discrete voltage value for each state, can be designed, but it would possess a very low reliability of operation. On the other hand, a circuit that has only two (ON or OFF) signal values can be constructed easily and is very reliable. Due to all these considerations, digital systems are constrained to take discrete values which are further constrained to take binary values.

Most digital circuits use two voltage levels labeled “Low” (0) and “High” (1). Often “Low” will be near 0 volts and “High” will be a higher depending on the supply voltage in use. The Below Fig. Shows a digital signal.

                         Most digital circuits use two voltage levels labeled

DIGITALTERMINOLOGY

Before going in further details of digital systems we shall first understand the basic terms and logics that are essential for the working of the digital electronics system.

(a) Logic Voltage Levels: Digital signals are represented by the two voltage levels which are referred to as logic voltage levels. A level logic is a logic in which the voltage levels represent logic 1 or logic O. There are two types of logics.

1. Positive Logic

2. Negative Logic

A positive logic system is the one in which higher of the two voltage levels rpresents the logic 1 and lower of the two voltage levels represents the logic O. A negative logic system is the one in which the lower of the two voltage levels represents the logic 1 and. the higher of the two voltage levels represent the logic O. So if two voltage levels are OV and +5V, then in the positive logic system, the OV represents a logic ‘0’ and the +5V represents a logic ‘1’. In negative logic system, it is the reverse, OV represents a logic’ l’ and +5V represents a logic ‘0’, (see in fig)

                       A positive logic system is the one in which higher of the two voltage levels represents the logic 1 and lower of the two voltage levels represents the logic O.

Unless or otherwise specified, all the signals are dealt with positive logic. Each logic gate is represented by a particular graphic symbol.

(b) Waveform: This refers to the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium. An instrument called oscilloscope can be used to pictorially represent the wave as a repeating image on a CRT or LCD screen. Some common periodic waveforms include sine waves, square wave etc. A digital waveform is generally in form of square wave.

(C) Digital Circuit: An electronic circuit that accepts and processes binary data according to the rules of Boolean logic (AND, OR NOT etc.) The simplest forms of digital circuits are built from logic gates, the building blocks of digital computer.

(d) Bit: Bit (‘Binary digit’) is a smallest unit of information storage and communication. It is the maximum amount of information that can be stored by a device or any other physical system that can normally exist in only two distinct states. These states are often interpreted as binary digits o and 1. They may also be interpreted as logical values, either true or false or two settings of a switch, either ‘on’ or ‘off’.

In modem computing devices, a bit is usually represented by an electrical voltage or current pulse, or by the electrical state of a flip-flop circuit. For devices using positive logic, a digit value of 1 is represented by a positive voltage relative to the electrical ground voltage (upto 5 volts in TTL designs), while a digit value of 0 is represented by 0 volts. In semiconductor memory, the two values of a bit may be represented by two levels of electrical charge stored in a capacitor.

(e) Nibble: It is equivalent to combination of four binary digits. For example: 1101, 1001, 1110 are all nibbles.

(I)Binary state terminology: The following table summarizes the binary state terminology.

 

The table summarizes the binary state terminology.

Analog System

By Dinesh Thakur

Most of the people are familiar with ordinary electrical circuits where voltages and currents can be measured with dial-type meters or analog meters as they are technically called. Such meters follow changes in voltage (or current) in a smooth step-less manner. This is what analog really means in electronics: signals or physical quantities which can vary in smooth-changing, a step-less manner. [Read more…] about Analog System