Convert the hexadecimal number 64cd to binary and then convert it from binary to octal
Answers
Answer:
(64CD)₁₆ = (110010011001101)₂ = (62315)₈
Step-by-step explanation:
Given hexadecimal number = 64CD
To convert it into binary, we will find the binary equivalent of each digit of the hexadecimal number and then write them together.
=> 6 = 0110
4 = 0100
C = 1100 (as C stands for 12)
D = 1101 (as D stands for 13)
=> (64CD)₁₆ = (110010011001101)₂
Since we cannot convert a binary number to octal, we will first convert it into decimal
=> 110010011001101 = 1*2⁰ + 0*2¹ + 1*2² + 1*2³ + 0*2⁴ + 0*2⁵ + 1*2⁶ + 1*2⁷ + 0*2⁸ + 0*2⁹ + 1*2¹⁰ + 0*2¹¹ + 0*2¹² + 1*2¹³ + 1*2¹⁴
= 1 + 0 + 4 + 8 + 0 + 0 + 64 + 128 + 0 + 0 + 1024 + 0 + 0 + 8192 + 16384
= 25805
Therefore, (110010011001101)₂ = (25805)₁₀
Now we will convert this decimal number to octal.
For this dividing 25805 by 8 and writing the remainders
8 25805 5
8 3225 1
8 403 3
8 50 2
8 6 6
0
Therefore, the octal equivalent is 62315
Therefore, (110010011001101)₂ = (25805)₁₀ = (62315)₈