Convert 374F in base 16 to octal​

33517

Method 1

Given:

374F in base 16

To convert to octal;

(i) convert each digit in the number to binary

3 = 0011

7 = 0111

4 = 0100

F = 1111

(ii) join the bits together starting from the first i.e

374F = 0011 0111 0100 1111

(iii) starting from the right to left, group the bits together, each group having 3 bits

374F = 0 011 011 101 001 111

(iv) the group with number of bits less than 3 should be padded with zero.

374F = 000 011 011 101 001 111

(v) convert each of the groups in (iv) above to decimal as follows:

000 = 0

011 = 3

011 = 3

101 = 5

001 = 1

111 = 7

(vi) combine the result above to get;

033517

The first zero can be removed

33517

Therefore, the number in octal is 33517₈

Method 2

Given:

374F in base 16

To convert to octal;

i) convert the number to decimal as follows;

a. Multiply each digit by 16 raised to the power of one less than their position starting from the leftmost digit.

=> 3 is at position 4, so we have

3 x 16⁴ ⁻ ¹ = 3 x 16³

=> 7 is at position 3, so we have

7 x 16³ ⁻ ¹ = 7 x 16²

=> 4 is at position 2, so we have

4 x 16² ⁻ ¹ = 4 x 16¹

=> F is at position 1, so we have

F x 16¹ ⁻ ¹ = F x 16⁰

b. Add each of the terms found in (a) together.

(3 x 16³) + (7 x 16²) + (4 x 16¹) + (F x 16⁰)

c. Remember that F = 15 in decimal. Therefore, substitute F = 15 into the result in (b)

(3 x 16³) + (7 x 16²) + (4 x 16¹) + (15 x 16⁰)

d. Solve the result in (c)

(3 x 4096) + (7 x 256) + (4 x 16) + (15 x 1)

12288 + 1792 +64 + 15

14159

Therefore,

374F in decimal is 14159

(b) Now convert the decimal to octal by dividing by 8 and noting the remainder.

8 | 14159

8 | 1769 r 7

8 | 221 r 1

8 | 27 r 5

8 | 3 r 3

  | 0 r 3

Taking the remainders from bottom up gives

33517₈

Therefore, the number in octal is 33517₈

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