Octal Decimal conversion Questions

Question 31. Convert the octal number 127 to decimal.

Solution: 87

• Write the place values: 1 × 8², 2 × 8¹, 7 × 8⁰.
• Calculate the powers: 1 × 64, 2 × 8, 7 × 1.
• Add the results: 64 + 16 + 7 = 87.

Question 32. Convert the decimal number 95 to octal.

Solution: 137

• Divide 95 by 8: 95 ÷ 8 = 11 remainder 7.
• Divide 11 by 8: 11 ÷ 8 = 1 remainder 3.
• Divide 1 by 8: 1 ÷ 8 = 0 remainder 1.
• Read remainders from bottom to top: 137.

Question 33. Convert the octal number 216 to decimal.

Solution: 142

• Write the place values: 2 × 8², 1 × 8¹, 6 × 8⁰.
• Calculate the powers: 2 × 64, 1 × 8, 6 × 1.
• Add the results: 128 + 8 + 6 = 142.

Question 34. Convert the decimal number 157 to octal.

Solution: 235

• Divide 157 by 8: 157 ÷ 8 = 19 remainder 5.
• Divide 19 by 8: 19 ÷ 8 = 2 remainder 3.
• Divide 2 by 8: 2 ÷ 8 = 0 remainder 2.
• Read remainders from bottom to top: 235.

Question 35. Convert the octal number 327 to decimal.

Solution: 215

• Write the place values: 3 × 8², 2 × 8¹, 7 × 8⁰.
• Calculate the powers: 3 × 64, 2 × 8, 7 × 1.
• Add the results: 192 + 16 + 7 = 215.

Question 36. Convert the decimal number 258 to octal.

Solution: 402

• Divide 258 by 8: 258 ÷ 8 = 32 remainder 2.
• Divide 32 by 8: 32 ÷ 8 = 4 remainder 0.
• Divide 4 by 8: 4 ÷ 8 = 0 remainder 4.
• Read remainders from bottom to top: 402.

Question 37. Convert the octal number 432 to decimal.

Solution: 282

• Write the place values: 4 × 8², 3 × 8¹, 2 × 8⁰.
• Calculate the powers: 4 × 64, 3 × 8, 2 × 1.
• Add the results: 256 + 24 + 2 = 282.

Question 38. Convert the decimal number 305 to octal.

Solution: 461

• Divide 305 by 8: 305 ÷ 8 = 38 remainder 1.
• Divide 38 by 8: 38 ÷ 8 = 4 remainder 6.
• Divide 4 by 8: 4 ÷ 8 = 0 remainder 4.
• Read remainders from bottom to top: 461.

Question 39. Convert the octal number 537 to decimal.

Solution: 351

• Write the place values: 5 × 8², 3 × 8¹, 7 × 8⁰.
• Calculate the powers: 5 × 64, 3 × 8, 7 × 1.
• Add the results: 320 + 24 + 7 = 351.

Question 40. Convert the decimal number 468 to octal.

Solution: 724

• Divide 468 by 8: 468 ÷ 8 = 58 remainder 4.
• Divide 58 by 8: 58 ÷ 8 = 7 remainder 2.
• Divide 7 by 8: 7 ÷ 8 = 0 remainder 7.
• Read remainders from bottom to top: 724.