33517
Step-by-step explanation:
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
