DECO_CSE_Lecture1[1].pdf

Digital Electronics and Computer Organization Instructor: Akhilesh Kumar Mishra (PhD, BITS Pilani) 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM...

Digital Electronics and Computer Organization Instructor: Akhilesh Kumar Mishra (PhD, BITS Pilani) 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM 1 School of Engineering, IILM Greater Noida, UP University  Number System: In the decimal number systems each of the ten digits, 0 through 9, represents a certain quantity. The position of each digit in a decimal number indicates the magnitude of the amount represented and can be assigned a weight. The weights for whole numbers are positive powers of ten that increase from right to left, beginning with 100 = 1 …………… 10³ 10² 10¹ 10º weighting factor of digit 7 3 4 6 = 7* 10³ + 3* 10² + 4* 10¹ +6* 10º (7346)10 = 7000 + 300 + 40 +6 =7346 Radix or base For fractional numbers, the weights are negative powers of ten that decrease from left to right beginning with 10¯¹. 10² 10¹ 10º. 10¯¹ 10¯² 10¯³ …….. (725.45)10 = (7 x 10²) + (2 x 10¹) + (5 x 10º) + (4 x 10-1) + (5 x 10-2) = 700 + 20 + 5 + 0.4 + 0.05 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM University 2 Bridging the Digital Divide Decimal-to-Binary Conversion Binary-to-Decimal Conversion 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM University 3  In Nibble there are 4-bit. In byte there are 8-bit. In One word there are 16-bit. Today most computers operate on 32-bit or 64 bit Processor. 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM University 4  Number System (Binary System): The binary system is less complicated than the decimal system because it has only two digits, it is a base-two system. The two binary digits (bits) are 1 and 0. The position of a 1 or 0 in a binary number indicates its weight, or value within the number, just as the position of a decimal digit determines the value of that digit. The weights in a binary number are based on the power of two: …………… 2³ 2² 2¹ 2º weighting factor of digit Largest decimal number = 2ⁿ - 1 1 1 1 1 = 1* 2³ + 1*2² + 1* 2¹ + 1* 2º (1111)2 = 8 + 4 + 2 +1 =15 Least Significant bit (LSB) (1110)2 = 8 + 4 + 2 +0 =14 (0111)2 = 0 + 4 + 2 +1 =7 Most Significant bit (MSB) 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM University 5  For fractional numbers, the weights are negative powers of 2 that decrease from left to right beginning with 2¯¹. 2² 2¹ 2º. 2¯¹ 2¯² 2¯³ …….. (101.11)2 = (1 x 2²) + (0 x 2¹) + (1 x 2º) + (1 x 2-1) + (1 x 2-2) = 4 + 0 + 1 + 0.5 + 0.25 (101.11)2 =5.75 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM University 6 Number System: Decimal Number System: (Base or Radix 10) The octal and hexadecimal number Digits required to represent= 0 to (base-1) systems have been introduced to Digits required to represent= 0 to (n-1) interpret large binary numbers in Digits required to represent 0 to 9 computer languages. Octal Number System: (Base or Radix 8) Digits required to represent 0 to 7 765 865 (765)8 = (7 x 8²) + (6 x 8¹) + (5 x 8º) =7*64 +48 +5 =448 +48 +5= 501 (765.11)8 = (7 x 8²) + (6 x 8¹) + (5 x 8º) + (1 x 8-1) + (1x 8-2) (765.11)8 = 501+ 0.125 + 0.015625 =501.140625 Hexadecimal Number System: (7E5)16 = (Base or Radix 16) Digits required to represent 0 to 15 (7E5)16 = = (7 x 16²) + (E x 16¹) + (5 x 16º) 0 to 9, 10, 11, 12, 13, 14 and 15 (7E5)16 = 7*256 + 14 x16 + 5 x1=2021 Digits required to represent 0 to 9, A, B, C, D, E and F 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM University 7  Number System Conversion: (1 1 1 1 1 1)2 (1* 25 + 1*24 + 1* 2³ + 1*2² + 1* 2¹ + 1* 2º) (32 + 16 + 8 + 4 + 2 + 1)10 (11111001)2 (10111101)2 (011111001)2 (010111101)2 (371)8 (275)8 (10110101)2 (10110101)2 (B5)16 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM University 8  Number System Conversion (Decimal to Binary): Remainder 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering, IILM University 9  THANK YOU Please reach me for any query@ Directors Block SVH (Cabin No.4, First Floor) Email: [email protected] 8/23/2024 Dr. Akhilesh Kumar Mishra, School of Engineering , IILM University 10