Octal To Decimal conversion Questions

Question 51. Convert the octal number 1674 to decimal.

Solution: 940

• Write the place values: 1 × 8³, 6 × 8², 7 × 8¹, 4 × 8⁰.
• Calculate the powers: 1 × 512, 6 × 64, 7 × 8, 4 × 1.
• Add the results: 512 + 384 + 56 + 4 = 940.

Question 52. Convert the decimal number 976 to octal.

Solution: 1700

• Divide 976 by 8: 976 ÷ 8 = 122 remainder 0.
• Divide 122 by 8: 122 ÷ 8 = 15 remainder 2.
• Divide 15 by 8: 15 ÷ 8 = 1 remainder 7.
• Divide 1 by 8: 1 ÷ 8 = 0 remainder 1.
• Read remainders from bottom to top: 1700.

Question 53. Convert the octal number 2043 to decimal.

Solution: 1075

• Write the place values: 2 × 8³, 0 × 8², 4 × 8¹, 3 × 8⁰.
• Calculate the powers: 2 × 512, 0 × 64, 4 × 8, 3 × 1.
• Add the results: 1024 + 0 + 32 + 3 = 1075.

Question 54. Convert the decimal number 1246 to octal.

Solution: 2346

• Divide 1246 by 8: 1246 ÷ 8 = 155 remainder 6.
• Divide 155 by 8: 155 ÷ 8 = 19 remainder 3.
• Divide 19 by 8: 19 ÷ 8 = 2 remainder 3.
• Divide 2 by 8: 2 ÷ 8 = 0 remainder 2.
• Read remainders from bottom to top: 2346.

Question 55. Convert the octal number 2514 to decimal.

Solution: 1332

• Write the place values: 2 × 8³, 5 × 8², 1 × 8¹, 4 × 8⁰.
• Calculate the powers: 2 × 512, 5 × 64, 1 × 8, 4 × 1.
• Add the results: 1024 + 320 + 8 + 4 = 1332.

Question 56. Convert the decimal number 1453 to octal.

Solution: 2645

• Divide 1453 by 8: 1453 ÷ 8 = 181 remainder 5.
• Divide 181 by 8: 181 ÷ 8 = 22 remainder 5.
• Divide 22 by 8: 22 ÷ 8 = 2 remainder 6.
• Divide 2 by 8: 2 ÷ 8 = 0 remainder 2.
• Read remainders from bottom to top: 2645.

Question 57. Convert the octal number 3017 to decimal.

Solution: 1551

• Write the place values: 3 × 8³, 0 × 8², 1 × 8¹, 7 × 8⁰.
• Calculate the powers: 3 × 512, 0 × 64, 1 × 8, 7 × 1.
• Add the results: 1536 + 0 + 8 + 7 = 1551.

Question 58. Convert the decimal number 1668 to octal.

Solution: 3204

• Divide 1668 by 8: 1668 ÷ 8 = 208 remainder 4.
• Divide 208 by 8: 208 ÷ 8 = 26 remainder 0.
• Divide 26 by 8: 26 ÷ 8 = 3 remainder 2.
• Divide 3 by 8: 3 ÷ 8 = 0 remainder 3.
• Read remainders from bottom to top: 3204.

Question 59. Convert the octal number 3325 to decimal.

Solution: 1773

• Write the place values: 3 × 8³, 3 × 8², 2 × 8¹, 5 × 8⁰.
• Calculate the powers: 3 × 512, 3 × 64, 2 × 8, 5 × 1.
• Add the results: 1536 + 192 + 16 + 5 = 1773.

Question 60. Convert the decimal number 1843 to octal.

Solution: 3513

• Divide 1843 by 8: 1843 ÷ 8 = 230 remainder 3.
• Divide 230 by 8: 230 ÷ 8 = 28 remainder 6.
• Divide 28 by 8: 28 ÷ 8 = 3 remainder 4.
• Divide 3 by 8: 3 ÷ 8 = 0 remainder 3.
• Read remainders from bottom to top: 3513.