number system.pptx
- 1. Number System in Digital Electronics Prof. Neeraj Bhargava Pooja Dixit Department of Computer Science, School of Engineering & System Sciences MDS University Ajmer, Rajasthan
- 2. • Definition: In digital electronics, the number system is used for representing the information. • The number system has different bases (radix) and the most common of them are the decimal, binary, octal, and hexadecimal. • Suppose if the number system representing the digit from 0 – 9 then the base of the system is the 10. • Types of Number Systems Some of the important types of number system are ▫ Decimal Number System (Base 10) ▫ Binary Number System (Base 10) ▫ Octal Number System (Base 10) ▫ Hexadecimal Number System (Base 10) What are Number System?
- 3. What are Number System? 1. Binary Number Systems • It uses only two digits 0 and1.The base of binary number system is 2 because it has only two digit 0 and 1. • The digital electronic equipments are works on the binary number system and hence the decimal number system is converted into binary system. • Note: 1 Byte= 8 Bit • 1 Bit=4 Nibble • Examples: • (10100)2, (11011)2, (11001)2, (000101)2, (011010)2. 2. Decimal Number Systems • The number system is having digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; this number system is known as a decimal number system because total ten digits are involved. The base of the decimal number system is 10.
- 4. What are Number System? 3. Octal Number System • The octal number system has base 8(means it has only eight digits from 0 to 7). • There are only eight possible digit values to represent a number. With the help of only three bits, an octal number is represented. Each set of bits has a distinct value between 0 and 7. • Examples: • (273)8, (5644)8, (0.5365)8, (1123)8, (1223)8. Number Octal Number 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111
- 5. What are Number System? 4. Hexadecimal Number System • The number system has a base of 16 means there are total 16 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F) used for representing a number. • The single-bit representation of decimal values10, 11, 12, 13, 14, and 15 are represented by A, B, C, D, E, and F. • Only 4 bits are required for representing a number in a hexadecimal number. • Examples: • (FAC2)16, (564)16, (0ABD5)16, (1123)16, (11F3)16. Binary Number Hexadecimal Number 0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 1110 E 1111 F
- 7. Number Base Conversion 1. Binary to Decimal Conversion • The process of converting binary to decimal is quite simple. The process starts from multiplying the bits of binary number with its corresponding positional weights. And lastly, we add all those products. • Let's take an example to understand how the conversion is done from binary to decimal. • Ex: 10101
- 8. Number Base Conversion 1. Ex: 111012 • Binary Number − 111012 = Decimal Number − 2910 Step Binary Number Decimal Number Step 1 111012 ((1 × 2 4 ) + (1 × 2 3 ) + (1 × 2 2 ) + (0 × 2 1 ) + (1 × 2 0 ))10 Step 2 111012 (16 + 8 + 4 + 0 + 1)10 Step 3 111012 2910
- 9. Binary to Decimal Conversion for Fractional Number • Ex: .0101
- 10. • Example 1: (10110.001)2 • We multiplied each bit of (10110.001)2 with its respective positional weight, and last we add the products of all the bits with its weight. • (10110.001)2=(1×24)+(0×23)+(1×22)+(1×21)+(0×20)+ (0×2-1)+(0×2-2)+(1×2-3) (10110.001)2=(1×16)+(0×8)+(1×4)+(1×2)+(0×1)+ (0×1⁄2)+(0×1⁄4)+(1×1⁄8) (10110.001)2=16+0+4+2+0+0+0+0.125 (10110.001)2=(22.125 )10
- 11. Binary to Decimal Conversion For Mixed Number Ex: 1101.101 After disregarding the weight 21 and 2-1 and on summing up the remaining weights the required decimal number is 13.625.
- 12. Questions convert the following binary numbers to decimal equivalents: A, 001100 B, 000011 C, 011100 D, 111100 E, 111111 Solutions: