Convert the decimal number 170 to binary

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Convert the decimal number 170 to binary: (Enter all bits next to each other and NO leading zeros!) D Question 2 Convert the hexadecimal number ABC to binary. (Enter all bits next to each other with leading zeros!) Question 3 What is the result of adding these two binary numbers: 10100 + 11 = Notes: . This is not conversion, answer binary number • Enter all bits next to each other and NO leading zeros!

The Correct Answer and Explanation is :

Let’s address each of your questions step by step:

Question 1: Convert the decimal number 170 to binary.

To convert the decimal number 170 to binary, we repeatedly divide the number by 2, recording the remainders:

  • 170 ÷ 2 = 85, remainder 0
  • 85 ÷ 2 = 42, remainder 1
  • 42 ÷ 2 = 21, remainder 0
  • 21 ÷ 2 = 10, remainder 1
  • 10 ÷ 2 = 5, remainder 0
  • 5 ÷ 2 = 2, remainder 1
  • 2 ÷ 2 = 1, remainder 0
  • 1 ÷ 2 = 0, remainder 1

Reading the remainders from bottom to top, we get: 10101010.

Question 2: Convert the hexadecimal number ABC to binary.

Each hexadecimal digit corresponds to a 4-bit binary number:

  • A (hex) = 1010 (binary)
  • B (hex) = 1011 (binary)
  • C (hex) = 1100 (binary)

Therefore, ABC (hex) = 101010111100 (binary).

Question 3: What is the result of adding these two binary numbers: 10100 + 11?

First, align the binary numbers:

  10100
+    11

Add them from right to left:

  • 0 + 1 = 1
  • 0 + 1 = 1
  • 1 + 0 = 1
  • 0 + 0 = 0
  • 1 + 0 = 1

The sum is 10111.

Explanation:

  • Decimal to Binary Conversion: The process involves dividing the decimal number by 2 and recording the remainders. This method is based on the fact that each division by 2 shifts the binary representation to the right, effectively determining each bit from least significant to most significant.
  • Hexadecimal to Binary Conversion: Hexadecimal is a base-16 system, and each digit represents four binary digits (bits). By converting each hexadecimal digit to its 4-bit binary equivalent, we can easily obtain the binary representation of the entire number.
  • Binary Addition: Binary addition follows the same principles as decimal addition but operates in base-2. The key rules are:
  • 0 + 0 = 0
  • 0 + 1 = 1
  • 1 + 0 = 1
  • 1 + 1 = 10 (which is 0 with a carry of 1)

Understanding these fundamental operations is crucial in computer science and digital electronics, as binary and hexadecimal systems are foundational to data representation and processing.

For a visual explanation of converting hexadecimal to binary, you might find the following video helpful:

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