Converting between binary, decimal and hexadecimal

Overview

Step-by-step methods and worked conversions between binary, decimal and hexadecimal, checking an answer, the largest value one byte holds, and a common conversion mistake explained.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Convert the binary number 10110101 to decimal.

   Model answer

   The decimal value is 181. The 1s sit in the 128, 32, 16, 4 and 1 columns, and 128 + 32 + 16 + 4 + 1 = 181.

2. 2

   Convert the binary number 00101100 to decimal.

   Model answer

   The decimal value is 44. The 1s sit in the 32, 8 and 4 columns, and 32 + 8 + 4 = 44.

3. 3

   Describe how to convert a decimal number to 8-bit binary.

   Model answer

   Write the place values from 128 down to 1. Put a 1 under each place value that fits into what remains, then subtract it. Every other place gets a 0.

4. 4

   Convert the decimal number 157 to 8-bit binary.

   Model answer

   The binary is 10011101. The number 157 is made from 128 + 16 + 8 + 4 + 1.

5. 5

   Convert the decimal number 90 to 8-bit binary.

   Model answer

   The binary is 01011010. The number 90 is made from 64 + 16 + 8 + 2.

6. 6

   How can you check a decimal-to-binary conversion?

   Model answer

   Add up the place values of every column that holds a 1. The total should equal the decimal number you started with.

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The same content, four other ways.

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