Question

show your work!
converting octal to decimal (1)
write each octal number as a decimal number.

1. octal = 11

decimal = 33
(with some handwritten breakdown steps)

1. octal = 13

decimal = 35
(with some handwritten breakdown steps)

1. octal = 1476

decimal =
(with some handwritten breakdown start)

1. octal = 1033

decimal =

1. octal = 434

decimal =

1. octal = 1557

decimal =

1. octal = 536

decimal =

1. octal = 1112

decimal =

1. octal = 20304

decimal =

1. octal = 6204

decimal =

Explanation:

Step1: Recall octal to decimal rule

For an octal number $d_n d_{n-1} ... d_1 d_0$, decimal = $\sum_{i=0}^{n} d_i \times 8^i$
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Problem 3: Octal = 1476

Step1: Assign digits to positions

Digits: $d_3=1, d_2=4, d_1=7, d_0=6$

Step2: Calculate each term

$1 \times 8^3 + 4 \times 8^2 + 7 \times 8^1 + 6 \times 8^0$
$= 1 \times 512 + 4 \times 64 + 7 \times 8 + 6 \times 1$

Step3: Sum the terms

$512 + 256 + 56 + 6 = 830$
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Problem 4: Octal = 1033

Step1: Assign digits to positions

Digits: $d_3=1, d_2=0, d_1=3, d_0=3$

Step2: Calculate each term

$1 \times 8^3 + 0 \times 8^2 + 3 \times 8^1 + 3 \times 8^0$
$= 1 \times 512 + 0 \times 64 + 3 \times 8 + 3 \times 1$

Step3: Sum the terms

$512 + 0 + 24 + 3 = 539$
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Problem 5: Octal = 434

Step1: Assign digits to positions

Digits: $d_2=4, d_1=3, d_0=4$

Step2: Calculate each term

$4 \times 8^2 + 3 \times 8^1 + 4 \times 8^0$
$= 4 \times 64 + 3 \times 8 + 4 \times 1$

Step3: Sum the terms

$256 + 24 + 4 = 284$
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Problem 6: Octal = 1557

Step1: Assign digits to positions

Digits: $d_3=1, d_2=5, d_1=5, d_0=7$

Step2: Calculate each term

$1 \times 8^3 + 5 \times 8^2 + 5 \times 8^1 + 7 \times 8^0$
$= 1 \times 512 + 5 \times 64 + 5 \times 8 + 7 \times 1$

Step3: Sum the terms

$512 + 320 + 40 + 7 = 879$
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Problem 7: Octal = 536

Step1: Assign digits to positions

Digits: $d_2=5, d_1=3, d_0=6$

Step2: Calculate each term

$5 \times 8^2 + 3 \times 8^1 + 6 \times 8^0$
$= 5 \times 64 + 3 \times 8 + 6 \times 1$

Step3: Sum the terms

$320 + 24 + 6 = 350$
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Problem 8: Octal = 1112

Step1: Assign digits to positions

Digits: $d_3=1, d_2=1, d_1=1, d_0=2$

Step2: Calculate each term

$1 \times 8^3 + 1 \times 8^2 + 1 \times 8^1 + 2 \times 8^0$
$= 1 \times 512 + 1 \times 64 + 1 \times 8 + 2 \times 1$

Step3: Sum the terms

$512 + 64 + 8 + 2 = 586$
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Problem 9: Octal = 20304

Step1: Assign digits to positions

Digits: $d_4=2, d_3=0, d_2=3, d_1=0, d_0=4$

Step2: Calculate each term

$2 \times 8^4 + 0 \times 8^3 + 3 \times 8^2 + 0 \times 8^1 + 4 \times 8^0$
$= 2 \times 4096 + 0 \times 512 + 3 \times 64 + 0 \times 8 + 4 \times 1$

Step3: Sum the terms

$8192 + 0 + 192 + 0 + 4 = 8388$
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Problem 10: Octal = 6204

Step1: Assign digits to positions

Digits: $d_3=6, d_2=2, d_1=0, d_0=4$

Step2: Calculate each term

$6 \times 8^3 + 2 \times 8^2 + 0 \times 8^1 + 4 \times 8^0$
$= 6 \times 512 + 2 \times 64 + 0 \times 8 + 4 \times 1$

Step3: Sum the terms

$3072 + 128 + 0 + 4 = 3204$

Answer:

1. 830
2. 539
3. 284
4. 879
5. 350
6. 586
7. 8388
8. 3204