Convert the following octal numbers to its decimal equivalent. Show your solutions. 4) 378 5) 7F3

Steps to Solve

1. Convert the first octal number (378) to decimal

To convert from octal to decimal, expand the number using powers of 8. The rightmost digit is multiplied by (8^0), the next by (8^1), and so on.

For the number (378_8):

[ 3 \times 8^2 + 7 \times 8^1 + 8 \times 8^0 ]

Calculating each term:

• (3 \times 8^2 = 3 \times 64 = 192)
• (7 \times 8^1 = 7 \times 8 = 56)
• (8 \times 8^0 = 8 \times 1 = 8)

Now, add them together:

[ 192 + 56 + 8 = 256 ]

2. Convert the second octal number (7F3) to decimal

Again, we expand the number using powers of 8:

However, the letter 'F' suggests a hexadecimal number; thus, we interpret this as an invalid octal digit. Let's assume the digits were intended to be valid octal digits between 0 and 7.

For the number (7F3):

We'll address the valid parts only. The only valid digit is (7) and (3):

Assuming (F) was a typo, let's convert (7\text{F}3_8) as (7\text{0}3_8).

[ 7 \times 8^2 + 0 \times 8^1 + 3 \times 8^0 ]

Calculating:

• (7 \times 8^2 = 7 \times 64 = 448)
• (0 \times 8^1 = 0)
• (3 \times 8^0 = 3 \times 1 = 3)

Now, adding these:

[ 448 + 0 + 3 = 451 ]