Understanding Binary Arithmetic in Digital Electronics Systems
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Binary Arithmetic Lecture by Dr. G.S. Virdi A comprehensive exploration of binary arithmetic in digital electronics, presented by Dr. G.S. Virdi, an accomplished expert with extensive experience in electronics engineering. This lecture, developed by a former professor and Director Grade scientist from the CSIR-Central Electronics Engineering Research Institute, offers in-depth insights into fundamental digital number systems and computational techniques. Key highlights: - Focused on Unit-1: Binary Arithmetic - Delivered by an experienced electronics engineering professional - Covers essential concepts in digital electronics and computational methods Ideal for students, researchers, and professionals in electrical engineering, computer science, and digital systems design.
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Understanding Binary Arithmetic in Digital Electronics Systems
- 1. Dr. G.S. Virdi Ex-Professor ECE DEPT. GGS- CMT Kharar Mohali Former Director grade scientist CSIR- central electronics engineering Research institute Pilani- 333931 India 1 UNIT-1- EE – Binary Arithmetic
- 2. 2 Thought of the Day G.S.Virdi G.S.Virdi
- 4. Binary Arithmetic Operations 1. Binary Addition 2. Binary Subtraction 1. 1’s Complement Subtraction 2. 2’s Complement Subtraction 3. Binary Multiplication 4. Binary Division G.S.Virdi G.S.Virdi
- 14. Decimal Addition Explanation 1 1 1 3 7 5 8 + 4 6 5 7 8 4 1 5 What just happened? 1 1 1 (carry) 3 7 5 8 + 4 6 5 7 8 14 11 15 (sum) - 10 10 10 (subtract the base) 8 4 1 5 So when the sum of a column is equal to or greater than the base, we subtract the base from the sum, record the difference, and carry one to the next column to the left.
- 15. Decimal Addition Explanation 1 1 1 3 7 5 8 + 4 6 5 7 8 4 1 5 What just happened? 1 1 1 (carry) 3 7 5 8 + 4 6 5 7 8 14 11 15 (sum) - 10 10 10 (subtract the base) 8 4 1 5 So when the sum of a column is equal to or greater than the base, we subtract the base from the sum, record the difference, and carry one to the next column to the left. G.S.Virdi G.S.Virdi
- 16. Binary Addition Rules Rules: 0 + 0 = 0 0 + 1 = 1 (just like in decimal) 1 + 0 = 1 1 + 1 = 210 = 102 = 0 with 1 to carry 1 + 1 + 1 = 310 = 112 = 1 with 1 to carry
- 17. 17 Binary Addition Col 7) Bring down the carried 1,Write 1 G.S.Virdi G.S.Virdi
- 30. Binary Subtraction Example 1 1 0 0 1 1 - 1 1 1 0 0 Example : Subtract binary 11100 from 110011 2 0 0 2 1 2 1 1 0 1 Col 1) Subtract 1 – 0 = 1 . Col 5) Try to subtract 0 – 1 can’t Must borrow from next column. Col 4) Subtract 1 – 1 = 0 Col 3) Try to subtract 0 – 1 can’t Must borrow 2 from next column.But next column is 0 so must go to column after next to borrow. the borrowed 2 to the 0 on the right. Now you can borrow from this column (leaving 1 remaining). Col 2) Subtract 1 – 0 = 1 Add the borrowed 2 to the original 0. Then subtract 2 – 1 = 1 1 Add the borrowed 2 to the remaining 0. Then subtract 2 – 1 = 1 Col 6) Remaining leading 0 can be ignored. G.S.Virdi G.S.Virdi
- 31. Binary Subtraction Verification 1 1 0 0 1 1 - 1 1 1 0 0 Verification 1100112 5110 - 111002 - 2810 2310 64 32 16 8 4 2 1 1 0 1 1 1 = 16 + 4 + 2 + 1 = 2310 1 1 0 1 1 Subtract binary 11100 from 110011: G.S.Virdi G.S.Virdi
- 32. Decimal Addition Explanation 1 1 1 3 7 5 8 + 4 6 5 7 8 4 1 5 What just happened? 1 1 1 (carry) 3 7 5 8 + 4 6 5 7 8 14 11 15 (sum) - 10 10 10 (subtract the base) 8 4 1 5 So when the sum of a column is equal to or greater than the base, we subtract the base from the sum, record the difference, and carry one to the next column to the left. G.S.Virdi G.S.Virdi
- 33. Binary Subtraction Example 1 0 1 0 0 1 - 1 0 1 0 0 Example 2: Subtract binary 10100 from 101001 2 0 0 2 1 1 0 1 0 Verification 1010012 4110 - 101002 - 2010 2110 64 32 16 8 4 2 1 1 0 1 0 1 = 16 + 4 + 1 = 2110 G.S.Virdi G.S.Virdi
- 34. Binary Subtraction Example 2 1 0 1 0 0 1 - 1 0 1 0 0 Example 2: Subtract binary 10100 from 101001 2 0 0 2 1 1 0 1 0 Verification 1010012 4110 - 101002 - 2010 2110 64 32 16 8 4 2 1 1 0 1 0 1 = 16 + 4 + 1 = 2110 G.S.Virdi G.S.Virdi
- 36. Binary Multiplication Multiplication can’t be that hard! It’s just repeated addition If we have adders, we can do multiplication also Remember that the AND operation is equivalent to multiplication on two bits: G.S.Virdi G.S.Virdi a b ab 0 0 0 0 1 0 1 0 0 1 1 1 a b a b 0 0 0 0 1 0 1 0 0 1 1 1
- 37. 37 Rules of Binary Multiplication G.S.Virdi G.S.Virdi
- 41. 41 Obtaining 2s complimentary number of Binary G.S.Virdi G.S.Virdi
- 47. Signed Multiplication 1 1 1 1 1 1 1 1 (-1)10 x 0 0 0 1 (+1)10 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 (-1)10 Sign extended G.S.Virdi G.S.Virdi
- 67. 0 0 0 0 1 1 1 1 Division of Unsigned Binary Integers 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 Quotient Dividend Remainder Partial Remainder 1 Divisor Partial Remainder 2 DiviQ:de 1 0 0 1 0 0 1 1 by 1 0 1 1 Quotient = 1 1 0 1 Remainder = 1 0 0 G.S.Virdi G.S.Virdi
- 68. 0 0 0 0 1 1 1 1 Division of Unsigned Binary Integers 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 Quotient Dividend Remainder Partial Remainder 1 Divisor Partial Remainder 2 Divide Q: 1 0 0 1 0 0 1 1 by 1 0 1 1 Quotient = 1 1 0 1 Remainder = 1 0 0 G.S.Virdi G.S.Virdi