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A positional-weighted system is one in which the values attached to the symbols depend on their location with respect to the radix point.
Binary, Octal, Decimal, and Hexadecimal are the commonly used positional-weighted number systems.
In a number, the extreme left digit is the MSD and the extreme right digit is the LSD
The Binary number system is used in digital systems because the devices used in digital systems operate in two states (ON and OFF) and the signals have two levels that are conveniently represented using the binary number system.
i)Bit: A binary digit is called a bit.
ii)Nibble: Each 4-bit binary group is called a nibble.
iii)Byte: Each 8-bit binary group is called a byte.
iv)Word: A group of bits processed by a digital system at a time is called a word.
The easiest way to convert large decimal numbers into binary and vice versa is via the hexadecimal system.
Subtraction in any number system with base b can be performed by using bβs complement method or (b-1)βs complement method.
In the sign-magnitude representation of numbers, the MSB is used to represent sign (0 for positive and 1 for negative) and the remaining bits represent the magnitude in straight binary form.
Hexadecimal code is widely used in digital systems because it is very convenient to enter binary data in a digital system using hex code.
To convert an octal number into binary, replace each octal digit with its 3-bit binary equivalent.
To convert a binary number into octal, starting from the binary point make groups of 3-bits on either side of the binary point and replace each 3-bit group with an octal digit. The required number of 0s can be added to the left of the integer part and to the right of the fraction part.
To convert a binary number into hex, starting from the binary point make groups of 4-bits on either side of the binary point and replace each 4-bit group with a hex digit.
To convert a hex number into binary, replace each hex digit by its 4-bit binary equivalent
The excess β 3 code of a decimal number is achieved by adding the number 3 to the 8421 code. It is the reflective code.
The gray code is the code where one bit will be different from the preceding number. For example, decimal numbers 13 and 14 are represented by gray code numbers 1011 and 1001, these numbers differ only in a single position that is the second position from the right. In the same way, the first position on the left changes for 7 and 8 which are 0100 and 1100, and this is also called the Unit-distance code. The gray code has a very special place in digital electronics.
The basic gates that make up the digital system are called logic gates. The circuit that can operate on many binary inputs to perform a particular logic function is called an electronic circuit.
There are three basic logic gates-
β AND gate.
β OR gate.
β NOT gate.
The Universal gates are NAND and NOR. The advantages of these gates are that they can be used for any logic calculation.
β NOT is the most simple logic gate.
β All it does is take in an input that is either ON or OFF and spits out the opposite.
β So for a 1, it will give a 0, and for a 0 it will give a 1.
β Another name for a NOT gate is inverter because it inverts (makes opposite) the input.
β Unlike NOT, AND needs two inputs
β It only turns on when both inputs are ON
β If only one input is on, it spits out OFF
β If both inputs are off, it spits out OFF
β OR also needs two inputs
β OR needs one input to be ON for it to spit out ON
β It is also ON when both inputs are ON
β It is OFF when both inputs are OFF
β XOR is the short way to say βExclusive ORβ
β Like OR, XOR also only needs one input to be ON for it to spit out ON
β But unlike OR, when both inputs are ON, XOR spits out OFF
β It is also OFF when both inputs are OFF
Computer architecture is the organization of the components which make up a computer system and the meaning of the operations which guide its function. It defines what is seen on the machine interface, which is targeted by programming languages and their compilers.
There are three categories of computer architecture, and all work together to make a machine function:
β System Design
β Instruction Set Architecture(ISA)
β Microarchitecture
The central computation concept of this architecture is that instructions and data are both loaded into the same memory unit, which is the main memory of the computer and consists of a set of addressable locations. The processor can then access the instructions and data required for the execution of a computer program using dedicated connections called buses β an address bus which is used to identify the addressed location and a data bus which is used to transfer the contents to and from a location.
Computer architecture | Computer organization |
---|---|
1. Architecture describes what the computer does | 1. The Organization describes how it does it. |
2. Computer Architecture deals with the functional behavior of computer systems. | 2. Computer Organization deals with a structural relationship. |
3. Architecture indicates its hardware | 3. Where Organization indicates its performance. |
There are various components of a computer:
i)Input
ii)CPU β Central Processing Unit
iii)ALU β Arithmetic Logic Unit
iv)CU β Control Unit
v)Memory Unit
vi)Output
Numeric codes used to represent decimal digits are called binary coded decimal (BCD) codes.
We are very comfortable with the decimal number system, but digital systems force us to use the binary system. Although the binary number system has many practical advantages and is widely used in digital computers, in many cases it is very convenient to work with decimal numbers especially when communication between man and machine is extensive. Since most of the numerical data generated by man are in decimal numbers, to simplify the communication process between man and machine BCD codes are used.
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