Digital Electronics

Decimal-to-Octal Conversion

The process of decimal-to-octal conversion is similar to that of decimal-to-binary conversion. The progressive division in the case of the integer part and the progressive multiplication while working on the fractional part here are by ‘8’ which is the radix of the octal number system. Again, the integer and fractional parts of the decimal number […]

Decimal-to-Binary Conversion

The integer and fractional parts are worked on separately. For the integer part, the binary equivalent can be found by successively dividing the integer part of the number by 2 and recording the remainders until the quotient becomes ‘0’. The remainders written in reverse order constitute the binary equivalent. For the fractional part, it is […]

Finding the Decimal Equivalent

The decimal equivalent of a given number in another number system is given by the sum of all the digits multiplied by their respective place values. The integer and fractional parts of the given number should be treated separately. Binary-to-Decimal, Octal-to-Decimal and Hexadecimal-to-Decimal conversions are illustrated below with the help of examples. Binary-to-Decimal Conversion Octal-to-Decimal […]

Hexadecimal-to-Decimal Conversion

The decimal equivalent of the hexadecimal number (1E0.2A)16 is determined as follows: The integer part = 1E0 The decimal equivalent = 0 × 160 + 14 × 161 + 1 × 162 = 0 + 224 + 256 = 480 The fractional part = 2A The decimal equivalent = 2 × 16−1 + 10 × […]

Octal-to-Decimal Conversion

The decimal equivalent of the octal number (137.21)8 is determined as follows: The integer part = 137 The decimal equivalent = 7 × 80 + 3 × 81 + 1 × 82 = 7 + 24 + 64 = 95 The fractional part = .21 The decimal equivalent = 2 × 8−1 + 1 × […]

Binary-to-Decimal Conversion

The decimal equivalent of the binary number (1001.0101)2 is determined as follows: The integer part = 1001 The decimal equivalent = 1 × 20 + 0 × 21 + 0 × 22 + 1 × 23 = 1 + 0 + 0 + 8 = 9 The fractional part = .0101 Therefore, the decimal equivalent […]

Number Representation in Binary & Sign-Bit Magnitude Method

Different formats used for binary representation of both positive and negative decimal numbers include the sign-bit magnitude method, the 1’s complement method and the 2’s complement method. Sign-Bit Magnitude Method In the sign-bit magnitude representation of positive and negative decimal numbers, the MSB represents the ‘sign’, with a ‘0’ denoting a plus sign and a ‘1’ […]

Common Terms used in Digital Number Systems

In this post you will find some commonly used terms with reference to different number systems. Terms used in Binary Number System Bit is an abbreviation of the term ‘Binary Digit’ and is the smallest unit of information. It is either ‘0’ or ‘1’. A byte is a string of eight bits. The byte is […]

Introduction to Hexadecimal Number System

The Hexadecimal Number System is a radix-16 number system and its 16 basic digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. The place values or weights of different digits in a mixed hexadecimal number are 160, 161, 162 and so on (for the integer […]

Introduction to Octal Number System

The octal number system has a radix of 8 and therefore has eight distinct digits. All higher-order numbers are expressed as a combination of these on the same pattern as the one followed in the case of the binary and decimal number systems described in “Introduction to Binary Number System“. The independent digits are 0, […]

Introduction to Binary Number System

The binary number system is a radix-2 number system with ‘0’ and ‘1’ as the two independent digits. All larger binary numbers are represented in terms of ‘0’ and ‘1’. The procedure for writing higher order binary numbers after ‘1’ is similar to the one explained in the case of the decimal number system. For […]

Introduction to Decimal Number System

The decimal number system is a radix-10 number system and therefore has 10 different digits or symbols. These are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. All higher numbers after ‘9’ are represented in terms of these 10 digits only. The process of writing higher order numbers after ‘9’ consists in […]

Introduction to Number Systems

Various number systems that are describing the parameters those are common to all number systems. An understanding of these parameters and their relevance to number systems is fundamental to the understanding of how various systems operate. Different characteristics that define a number system include the number of independent digits used in the number system, the […]

Introduction to Analogue versus Digital

There are two basic ways of representing the numerical values of the various physical quantities with which we constantly deal in our day-to-day lives. Analogue Digital Introduction to Analogue Analogue is to express the numerical value of the quantity as a continuous range of values between the two expected extreme values. For example, the temperature […]