Presentation on Number System

Types of Number System Non-Positional number system

Non-Positional Number System Symbol represents the value regardless of its position. Difficult to perform arithmetic operation. For example:- I, II, III, IV, V, VI, VII, VIII, IX, X XI,XII, XIII, XIV, XV, XVI, XVII, XVIII, XIX, XX

Positional Number System Symbols represent different values depending upon the position. The values of each digit is determined by:- - Digit itself - Position of the digit - Base of the number system

Decimal number The base is equal to 10 Uses 10 different symbols.

Continue… =2000 + 500 + 80 + 6 =2586 For example: (2*1000) + (5*100) + (8*10) + (6*1) =2000 + 500 + 80 + 6 =2586

Bit Binary digit 0 or 1 Smallest possible unit of data Work with a group of bits.

Byte Group of eight bits Used to represent one character

Binary Number System The base is 2. Each position represents a power of the base 2. For example:-Conversion from 00111101 to decimal is-

Octal Number System The base is 8 Largest single digit is 7 For example:- decimal equivalent to the octal number 421 is 273

Hexadecimal Number System The base is 16 Combination of 0-9 and A-F For example:-Decimal equivalent to the hexadecimal number 1421 is 1057

Decimal, binary and hexadecimal representations

Conversion of decimal representation to binary Determine the binary equivalent of 3610 2 36 18 9 4 1 Remainder 1 Least Significant Bit (LSB) Most significant Bit (MSB)

Continue… Taking remainders in reverse order, we have 100100

Conversion of binary representation to decimal = 16 + 8 + 0 + 2 + 0 = 26

Conversion of hexadecimal to binary Each hexadecimal digit is equivalent to 4 binary digits. For example:-binary equivalent to 2C :- 2 C = 0010 1100 2C = 001011002(in binary)

Conversion binary to hexadecimal The binary digits are arranged in groups of 4 starting from the right. For example:-Convert 0011 0100 0110 to hexadecimal 0011 0100 0110 3 4 6 (001101000110) 2 = (346 )16

Conversion of decimal representation to hexadecimal (5112)10 Remainder 8 = 8 15=F 3=3 1=1 16 5112 319 19 1 Least significant bit (LSB) Most significant bit (MSB) (5112)10=(13F8)16

Conversion of hexadecimal representation to decimal 163 162 161 160 4096 256 16 1 B 6 E 11*256 + 6*16 +14*1 = 2816 + 96 + 14 = (2926) 10

Conversion of octal representation to hexadecimal Convert each octal digit to 3-bit binary form Combine all the 3 bits binary form Divide the binary numbers into the 4-bit binary form Convert these 4 bits blocks into their respective hexadecimal symbols

Continue… Example (2327)8 2 3 7 Octal Number Binary Coded value 010 011 111 Combining 3-bit blocks we have 010011010111 Dividing of binary numbers into 4-bit binary blocks and converting these blocks into their respective hexadecimal symbols, we have: 0100 1101 0111 4 D 7

Conclusion Same procedure to convert decimal numbers to binary, octal & hexadecimal Same procedure to convert from binary, octal & hexadecimal to decimal numbers