number system

Number System

A way of representing and expressing numbers.

Decimal Number System

A base-10 system that uses ten digits (0-9) to represent numbers.

Binary Number System

A base-2 system that uses only two digits (0 and 1) to represent numbers.

Octal Number System

A base-8 system that uses eight digits (0-7) to represent numbers.

Hexadecimal Number System

A base-16 system that uses sixteen digits (0-9 and A-F) to represent numbers.

Conversion from Decimal to Any Other Base

Dividing a decimal number by the desired base repeatedly and noting down the remainders to form the equivalent number in the desired base.

Conversion from Binary to Octal

Grouping binary digits into sets of three and replacing each set with its equivalent octal digit.

Conversion from Binary to Hexadecimal

Grouping binary digits into sets of four and replacing each set with its equivalent hexadecimal digit.

Conversion from Hexadecimal to Binary

Replacing each hexadecimal digit with its equivalent four-digit binary representation.

Octal to Hex

Converting octal digits into sets of three from right to left and replacing each group with its equivalent hexadecimal digit.

Binary Fractions

Fractional numbers represented in the binary number system.

Decimal to Binary Fractions

Multiplying the decimal fraction by 2 and noting the integer part of the result.

Decimal Fractions to Octal

Multiplying the decimal fraction by 8 and noting the integer part of the result.

Octal Fraction to Decimal

Multiplying each digit of the octal fraction by the corresponding power of 8 and summing the results.

Binary Arithmetic

Performing arithmetic operations (addition, subtraction, multiplication, division) on binary numbers.

Sign Numbers

A way to represent positive and negative values in binary form using the most significant bit (MSB) as the sign bit.

One's Complement

Inverting all the bits of a binary number to represent negative numbers.

Two's Complement

Inverting all the bits of a binary number and adding 1 to the least significant bit to represent both positive and negative numbers.

Single Precision Floating Point Number Representation

A method to represent real numbers in a computer system using 32 bits and consisting of a sign bit, exponent, and mantissa.

Decimal to Binary Conversion

Dividing a decimal number by 2 repeatedly and noting down the remainders in reverse order to obtain the binary representation.

Binary to Decimal Conversion

Assigning weights to each bit of a binary number and summing up the products to obtain the decimal representation.

Data Representation

Methods and techniques used to represent and store data in a computer system, including binary system, numeric representation, and character representation.