If '100' in base-2 is equal to '4' in decimal, what is '110' in base-2?

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Question: If \'100\' in base-2 is equal to \'4\' in decimal, what is \'110\' in base-2?

Options:

Correct Answer: 5

Solution:

\'110\' in base-2 = 1*2^2 + 1*2^1 + 0*2^0 = 4 + 2 + 0 = 6.

If '100' in base-2 is equal to '4' in decimal, what is '110' in base-2?

If '100' in base-2 is equal to '4' in decimal, what is '110' in base-2?

Step 1: Understand that '110' is a number in base-2 (binary).
Step 2: Break down '110' into its individual digits: 1, 1, and 0.
Step 3: Assign each digit a power of 2 based on its position from right to left: the rightmost digit is 2^0, the next is 2^1, and the leftmost is 2^2.
Step 4: Calculate the value of each digit: the leftmost '1' is 1*2^2, the middle '1' is 1*2^1, and the '0' is 0*2^0.
Step 5: Perform the calculations: 1*2^2 = 4, 1*2^1 = 2, and 0*2^0 = 0.
Step 6: Add the results together: 4 + 2 + 0 = 6.
Step 7: Conclude that '110' in base-2 is equal to '6' in decimal.

Binary to Decimal Conversion – Understanding how to convert binary numbers (base-2) to decimal (base-10) using powers of 2.