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Binary-Arithmeticcccccccccccccccccc.pptx
- 2. Binary operations Binary addition Binary subtraction Binary multiplication Binary division
- 3. Binary addition Rules for binary addition:
- 5. Addition of large binary numbers
- 7. Solve 1. (12)10 + (8)10 2. (15)10 + (10)10 3. (35)10 + (48)10 4. (10101)2 + (10110)2 5. (10111)2 + (11000)2
- 9. Rules for binary subtraction
- 11. Subtraction of large binary numbers 11001 - 10111 = 00010
- 12. Examples
- 13. Binary subtraction Example 1: 0011010 001100 Solution: 1 1 Borrow 0 0 1 1 0 1 0 (-) 0 0 1 1 0 0 0 0 0 1 1 1 0 Decimal Equivalent : 0 0 1 1 0 1 0 = 26 0 0 1 1 0 0 = 12 Therefore, 26 12 = 14 The binary resultant 0 0 0 1 1 1 0 is equivalent to the 14
- 14. Logic for binary to decimal 0 0 1 1 0 1 0 =26 26 25 24 23 22 21 20 64 32 16 8 4 2 1 16 8 2 =26
- 15. Binary Subtraction Example 2: 0100010 0001010 Solution: 1 1 Borrow 0 1 0 0 0 1 0 = 3410 (-) 0 0 0 1 0 1 0 = 1010 0 0 1 1 0 0 0 = 2410
- 16. Binary subtraction subtract 1010101.10 from 1111011.11 1 borrow 1111011.11 1010101.10 0100110.01
- 17. Binary subtraction using 1s and 2s complement method
- 18. How to find 1s Complement of given number 1s complement of a number is found by changing all 1s to 0s and all 0s to 1s. Ex: 1s complement of a number 10111 is = 01000 Solve---- Find 1s complement of a. 11010 = 00101 b. 101101= 010010 c. 1010= 0101 d. 1111=0000 e. 1011001=0100110
- 19. How to find 2s Complement of given number The 2s complement of a number is obtained by adding 1 to the LSB of 1s complement of that number 2s complement = 1s complement + 1 Ex: obtain 2s complement of a number (10110010)2 Solution:
- 20. Solve Find 2s complement of following numbers. a. (1101)2 0010=1=0011 b. (10111)2 01000+1=01001 c. (101101)2 010010+1=010011 d. (1011111)2 010000+1=010001 e. (101111101)2 010000010+1=010000011
- 21. Subtraction using 1s complement A) For subtracting a smaller number from a larger number, the 1s complement method is as follows: 1. Determine the 1s complement of the smaller number. 2. Add the 1s complement to the larger number. 3. Remove the final carry and add it to the result. This is called the end-around carry.
- 22. Binary subtraction using 1s complement method To perform subtraction (A)2 - (B)2 Step 1: convert number to be subtracted (B)2 to its 1s complement. Step 2: Add first number (A)2 and 1s complement of (B)2 using rules of binary addition. Step 3: if final carry is 1 then add it to the result of addition obtained in step 2 to get final result. **If final carry in step 2 is 1 then result obtained in step 2 is Positive and in its true form no conversion required. Step 4: if final carry in step 2 is 0 then result obtained in step 2 is negative and in 1s complement form. So convert it to its true form.
- 23. Binary subtraction using 1s complement 10---------------------------------- 10 -3 - 11-----1complement of 11 +00 --- ----- -1 10 result 1s complement of result 01 final result carry 0 so result sign is negative 0
- 24. 3 11 11 -2 10---------01 ---------- 1 0 0 1 ------------ 01
- 25. Binary subtraction using 1s complement 9 1001 1001 - 15 1111 1s complement +0000 ------- ------- -6 1001 1s complement of result 0110 ---6 carry is 0 so result sign is negative 0
- 26. Binary Subtraction Questions Using 1s Complement Question 1: (110101)2 (100101)2 Solution: (1 1 0 1 0 1)2 = 5310------- minuend. (1 0 0 1 0 1)2 = 3710 subtrahend Now take the 1s complement of the subtrahend and add with minuend. 1 carry 1 1 0 1 0 1 (+) 0 1 1 0 1 0 0 0 1 1 1 1 + 1 carry 0 1 0 0 0 0 Therefore, the solution is 010000 (010000)2 = 1610 1
- 27. Binary Subtraction Questions Using 1s Complement Question 2: (101011)2 (111001)2 43-57= -14 Solution: Take 1s complement of the subtrahend 1 1 1 1 0 1 0 1 1 (+) 0 0 0 1 1 0 (1s complement) 1 1 0 0 0 1 Now take the 1s complement of the resultant since it does not carry 1 The resultant becomes 0 0 1 1 1 0 Now, add the negative sign to the resultant value Therefore the solution is (001110)2.
- 28. Binary subtraction using 2s complement method To perform subtraction (A)2 - (B)2 Step 1: convert number to be subtracted (B)2 to its 2s complement. Step 2: Add first number (A)2 and 2s complement of (B)2 using rules of binary addition. Step 3: if final carry is 1 then the result Positive and in its true form no conversion required. Step 4: if final carry in step 2 is 0 then result obtained in step 2 is negative and in 2s complement form. So convert it to its true form. ** Carry always be discarded.
- 29. Binary subtraction using 2s complement 5 101 -7 111 1s comple.---000 ---- + 1 -2 ------ 2s complement 001 +101 ------- result 110 1s complement 001 + 1 -------- 2s complement 010 final result Carry is 0 so result is negative 0
- 30. 13 1101 -10 1010 0101 ------- 1 03 --------- 0110 1101 -------------- 1 0011
- 31. Subtraction using 2s complement 33 100001 -45 101101 1s 010010 ----- + 1 -12 ------------ 2s 010011 +100001 ------------ 110100 result 1s 001011 + 1 ------------- 2s 001100 final result 0
- 32. Solve the following binary subtraction using 1s and 2s complement method 15-23 25-18 23-18 18-9
- 34. 10111 10111 -10010 01101 1s 1 --------- 01110 10111 ----------- 100101
- 36. Multiplication (1 of 3) Decimal (just for fun) 35 x 105 175 000 35 3675
- 37. Multiplication Binary, two 1-bit values A B A B 0 0 0 0 1 0 1 0 0 1 1 1
- 38. Example Binary Multiplication A = 910 = 10012 A3A2A1A0 B = 810 = 10002 B3B2B1B0 1001 1000 ------------------ 0000 multiply by B0 + 0000 multiply by B1 + 0000 multiply by B2 + 1001 multiply by B3 -------------- 1001000 Cross check 1 0 0 1 0 0 0 64 32 16 8 4 2 1 place value of result bits 64+8=72
- 39. Perform the following multiplication in binary number system: 10112 1012 1 0 1 1 1 0 1 --------- 1 0 1 1 + 0 0 0 0 + 1 0 1 1 carry 1 ------------------- 1 1 0 1 1 1
- 40. Perform the following multiplication in binary number system: 101.12 11.12 1 0 1 .1 1 1 .1 ---------------- 1 0 1 1 + 1 0 1 1 + 1 0 1 1 Carry 1 1 1 1 --------------------- 1 0 0 1 1. 0 1
- 41. Multiplication Binary, two n-bit values As with decimal values E.g., 1110 x 1011 1110 1110 0000 1110 10011010
- 42. Binary Multiplication Perform the following multiplication in binary number system: 1510 810 Perform the following multiplication in binary number system: 10012 11012 Perform the following multiplication in binary number system: 111.112 101.12
- 43. Solve (205)10 x (3)10 (1110101)2 x (1001)2 (110)2 x (10)2 (1111101)2 x (101)2 (15)10 x (8)10
- 44. Binary Division
- 45. Binary Division:110 歎10 10) 110 ( 11 - 10 ---------- 010 - 10 ------------ 000
- 46. Binary division Ex: (25)10 歎 (5)10
- 47. Perform the division 111110.1 歎101 1100.1 quotient 101) 111110.1 5)62.5(12.5 -101 -5 -------------- --------- 0101 12.5 - 101 - 10 ------------- -------- 0000101 02.5 - 101 - 2.5 -------------- -------- 0000000 remainder 000
- 48. Solve (205)10 歎 (3)10 (1110101)2 歎 (1001)2 (110)2 歎 (10)2 (1111101)2 歎 (101)2
- 50. 100)1100(11 100 --------------- 0100 100 ---------------- 0000
- 51. END