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Number systems Octal (Base 8) ses digits: 0-7 Decimal (Base 10 Uses digit.

Number Systems Decimal Counting using fingers Base 10 System (0-9) Binary Hexadecimal Octal To shorten long binary numbers Base 8 (0-7) For computers-since flip flops store either 0 or 1 Base 2 (0,1) Since data is stored in bytes Base 16 (0-9, A-F).

Decimal Number System. The decimal number system is a base-10 system that uses the digits 0–9 to represent numbers. It is the most commonly used system for representing and manipulating numbers in modern mathematics. Here are some characteristics of the decimal number system: Each value in the number system has a place value of power 10. Each digit has a value based on its position, called place value. The decimal system also requires a dot (decimal point) to represent decimal fractions..

Binary Number System. At the heart of all digital systems, the binary number system uses only two digits (0 and 1) to represent numbers and perform logical operations. A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation..

Octal Number System. A base-8 number system commonly used in computer programming, octal simplifies binary representation by grouping digits in sets of three. The octal number system is a number system of base 8 which means that 8 different symbols are needed to represent any number in the octal system. The symbols are 0, 1, 2, 3, 4, 5, 6, and 7. The smallest two-digit number in this system is (10)8 ( 10 ) 8 which is equivalent to decimal 8..

Hexadecimal Number System. Derived from the Latin word "hex," meaning six, the hexadecimal system utilizes 16 symbols (0-9, A-F) to efficiently represent large binary numbers. The hexadecimal number system is a type of number system, that has a base value equal to 16. It is also pronounced sometimes as 'hex'. Hexadecimal numbers are represented by only 16 symbols. These symbols or values are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. Each digit represents a decimal value..

Comparison of Number Systems. Representation. Each number system has its unique representation, impacting the size, readability, and interpretation of values..

Common Uses of Number Systems in Computer Architecture.

Ones Complement & Twos Complement. 1 's Complement Addition Using I's complement numbers, adding numbers is easy. • For example, we want to add +(1100)2 and • Let's compute (12)10 + (1)10. (12)10 = 011002 in I's comp. (1)10 = = 000012 in I's comp. • Step I: Add binary numbers Step 2: Add carry to low-order bit Add carry 00001 o ' 01.

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