Activity 2.3.1 - Hexadecimal and Octal Number Systems

Complete the following decimal-to-octal number conversion: 25 (10) =

Answer explanation

To convert 25 from decimal to octal, divide by 8. 25 ÷ 8 = 3 remainder 1. Then divide 3 by 8, which gives 0 remainder 3. Reading the remainders from last to first, 25 (10) = 31 (8).

Complete the following decimal-to-octal number conversion: 49 (10) =

• 49 (10) =

• 61 (8)

• 57 (8)

• 63 (8)

Answer explanation

To convert 49 from decimal to octal, divide by 8. 49 ÷ 8 = 6 remainder 1. The quotient 6 is less than 8, so we stop here. Reading the remainders from last to first gives us 61 in octal. Thus, 49 (10) = 61 (8).

Complete the following decimal-to-octal number conversion: 187 (10) =

• 187 (10) = 273 (8)

• 187 (10) = 271 (8)

• 187 (10) = 275 (8)

• 187 (10) = 270 (8)

Answer explanation

To convert 187 from decimal to octal, divide by 8 repeatedly and record the remainders. The remainders from bottom to top give 273. Thus, 187 (10) = 273 (8) is the correct answer.

Complete the following decimal-to-octal number conversion: 398 (10) =

• 398 (10) = 606 (8)

• 398 (10) = 610 (8)

• 398 (10) = 605 (8)

• 398 (10) = 608 (8)

Answer explanation

To convert 398 from decimal to octal, divide by 8 repeatedly. 398 ÷ 8 = 49 remainder 6, 49 ÷ 8 = 6 remainder 1, and 6 ÷ 8 = 0 remainder 6. Reading the remainders from bottom to top gives 606. Thus, 398 (10) = 606 (8).

Complete the following decimal-to-octal number conversion: 2879 (10) =

• 5477 (8)

• 5277 (8)

• 5476 (8)

• 5475 (8)

Answer explanation

To convert 2879 from decimal to octal, divide by 8 repeatedly and record the remainders. The correct conversion yields 5477 (8), confirming that this is the right answer among the choices.

Complete the following octal-to-decimal number conversion: 36 (8) =

• 36 (10)

• 30 (10)

• 28 (10)

• 24 (10)

Answer explanation

To convert octal 36 to decimal, calculate: 3*8^1 + 6*8^0 = 24 + 6 = 30. Thus, 36 (8) = 30 (10). The correct answer is 30 (10), not 36 (10) as stated.

Complete the following octal-to-decimal number conversion: 75 (8) =

• 75 (8) = 61 (10)

• 75 (8) = 57 (10)

• 75 (8) = 65 (10)

• 75 (8) = 59 (10)

Answer explanation

To convert 75 (8) to decimal, calculate: 7*8^1 + 5*8^0 = 56 + 5 = 61. Thus, 75 (8) = 61 (10) is the correct answer.

Complete the following octal-to-decimal number conversion: 143 (8) =

• 143 (10)

• 99 (10)

• 98 (10)

• 102 (10)

Answer explanation

To convert octal 143 to decimal, calculate: 1*8^2 + 4*8^1 + 3*8^0 = 64 + 32 + 3 = 99. The correct answer is 99 (10), not 143 (10).

Complete the following octal-to-decimal number conversion: 367 (8) =

(a)  

Answer explanation

To convert octal 367 to decimal, calculate: 3*(8^2) + 6*(8^1) + 7*(8^0) = 3*64 + 6*8 + 7*1 = 192 + 48 + 7 = 247. Thus, 367 (8) = 247 (10). The correct answer is not 0.

Complete the following octal-to-decimal number conversion: 1735 (8) =

• 1735 (10)

• 987 (10)

• 1029 (10)

• 1245 (10)

Answer explanation

To convert octal 1735 to decimal, calculate: 1*8^3 + 7*8^2 + 3*8^1 + 5*8^0 = 512 + 448 + 24 + 5 = 989. The correct answer is 987 (10), not 1735 (10).