Octal To Decimal conversion Questions

Question 41. Convert the octal number 645 to decimal.

Solution: 421

• Write the place values: 6 × 8², 4 × 8¹, 5 × 8⁰.
• Calculate the powers: 6 × 64, 4 × 8, 5 × 1.
• Add the results: 384 + 32 + 5 = 421.

Question 42. Convert the decimal number 550 to octal.

Solution: 1046

• Divide 550 by 8: 550 ÷ 8 = 68 remainder 6.
• Divide 68 by 8: 68 ÷ 8 = 8 remainder 4.
• Divide 8 by 8: 8 ÷ 8 = 1 remainder 0.
• Divide 1 by 8: 1 ÷ 8 = 0 remainder 1.
• Read remainders from bottom to top: 1046.

Question 43. Convert the octal number 761 to decimal.

Solution: 497

• Write the place values: 7 × 8², 6 × 8¹, 1 × 8⁰.
• Calculate the powers: 7 × 64, 6 × 8, 1 × 1.
• Add the results: 448 + 48 + 1 = 497.

Question 44. Convert the decimal number 631 to octal.

Solution: 1177

• Divide 631 by 8: 631 ÷ 8 = 78 remainder 7.
• Divide 78 by 8: 78 ÷ 8 = 9 remainder 6.
• Divide 9 by 8: 9 ÷ 8 = 1 remainder 1.
• Divide 1 by 8: 1 ÷ 8 = 0 remainder 1.
• Read remainders from bottom to top: 1177.

Question 45. Convert the octal number 1042 to decimal.

Solution: 546

• Write the place values: 1 × 8³, 0 × 8², 4 × 8¹, 2 × 8⁰.
• Calculate the powers: 1 × 512, 0 × 64, 4 × 8, 2 × 1.
• Add the results: 512 + 0 + 32 + 2 = 546.

Question 46. Convert the decimal number 689 to octal.

Solution: 1261

• Divide 689 by 8: 689 ÷ 8 = 86 remainder 1.
• Divide 86 by 8: 86 ÷ 8 = 10 remainder 6.
• Divide 10 by 8: 10 ÷ 8 = 1 remainder 2.
• Divide 1 by 8: 1 ÷ 8 = 0 remainder 1.
• Read remainders from bottom to top: 1261.

Question 47. Convert the octal number 1153 to decimal.

Solution: 627

• Write the place values: 1 × 8³, 1 × 8², 5 × 8¹, 3 × 8⁰.
• Calculate the powers: 1 × 512, 1 × 64, 5 × 8, 3 × 1.
• Add the results: 512 + 64 + 40 + 3 = 627.

Question 48. Convert the decimal number 743 to octal.

Solution: 1347

• Divide 743 by 8: 743 ÷ 8 = 92 remainder 7.
• Divide 92 by 8: 92 ÷ 8 = 11 remainder 4.
• Divide 11 by 8: 11 ÷ 8 = 1 remainder 3.
• Divide 1 by 8: 1 ÷ 8 = 0 remainder 1.
• Read remainders from bottom to top: 1347.

Question 49. Convert the octal number 1372 to decimal.

Solution: 746

• Write the place values: 1 × 8³, 3 × 8², 7 × 8¹, 2 × 8⁰.
• Calculate the powers: 1 × 512, 3 × 64, 7 × 8, 2 × 1.
• Add the results: 512 + 192 + 56 + 2 = 746.

Question 50. Convert the decimal number 857 to octal.

Solution: 1521

• Divide 857 by 8: 857 ÷ 8 = 107 remainder 1.
• Divide 107 by 8: 107 ÷ 8 = 13 remainder 3.
• Divide 13 by 8: 13 ÷ 8 = 1 remainder 5.
• Divide 1 by 8: 1 ÷ 8 = 0 remainder 1.
• Read remainders from bottom to top: 1521.