To represent a decimal number 35 in binary, the minimum number of bits...
To represent a decimal number 35 in binary, the minimum number of bits required are 6. Its binary representation is 100011.
View all questions of this test
To represent a decimal number 35 in binary, the minimum number of bits...
To represent a decimal number 35 in binary, we need to convert it from base 10 to base 2. The base 10 system uses 10 digits (0-9), while the base 2 system (binary) uses only 2 digits (0 and 1).
To determine the minimum number of bits required to represent a decimal number in binary, we can use the formula:
n = ceil(log2(x+1))
Where 'x' is the decimal number and 'n' is the number of bits required.
Let's calculate the number of bits required to represent 35 in binary:
Step 1: x = 35
Step 2: n = ceil(log2(35+1))
Step 3: n = ceil(log2(36))
Step 4: n = ceil(5.169925)
Step 5: n = 6
Therefore, the minimum number of bits required to represent the decimal number 35 in binary is 6.
Explanation:
- Decimal number 35 has a maximum value of 35 in the base 10 system.
- To convert it into binary, we need to find the number of bits required to represent a value up to 35.
- Using the formula mentioned above, we calculate the number of bits required as 6.
- This means that we need a 6-bit binary number to represent the decimal number 35.
- The binary representation of 35 is 100011 in 6 bits.
- Each bit in the binary representation represents a power of 2, starting from the rightmost bit as 2^0, then 2^1, 2^2, and so on.
- By summing up the values of the bits that are set to 1 (in this case, the 6th bit and the 1st bit), we get the decimal value 35.
Therefore, the correct answer is option 'A' (6 bits).