Practice Problems


Let's start by doing a sample problem together. Remember, A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15 in hexadecimal. As you work through the practice problems, your job is to fill in the boxes with the yellow backgrounds as I've done in the example problem below.

Example Problem


Figure 1

Our hexadecimal number is A1D0. Let's start with A. A is in the 4096s column so we multiply A, which is 10 × 4096 = 40,960. Then, we have to reproduce this value in the binary columns directly below A (the columns 32768, 16384, 8192, and 4096). The answer is 1010 in those columns because 1 × 32768 + 1 × 8192 = 40,960, just like in the hexadecimal column above it.

Next, we move to the 1 in the 256s column. 1 × 256 = 256 and so the same. Then we reproduce that computed value in the next 4 binary bits (2048, 1024, 512, and 256). The answer is 0001 because the 256 in the binary column = the 256 in the hexadecimal column above it.

Then, we move to the D in the 16s column. D = 13, so we have 13 × 16 = 208 and do the same. We reproduce 208 in the next 4 binary bits (128, 64, 32, and 16). The answer is 1101 because the 128 + 64 + 16 in those binary columns = 208, the value we computed in the hexadecimal column above.

Finally, we have a 0 in the 1s column. 0 × 1 = 0 and of course 0 in the hexadecimal 1s column = 0 in the next 4 binary bits. The answer is 0000.

So, A1D0 in hexadecimal = 1010 0001 1101 0000 in binary.

Now, you try it. Some of the practice problems will require you to convert hexadecimal to binary, and others will require you to convert binary to hexadecimal. When you are finished, scroll to the bottom of the page for the answers.

Problem 1


What is hexadecimal 5E4A in binary?

Figure 2

Problem 2


What is hexadecimal 5F4 in binary?

Figure 3

Problem 3


What is hexadecimal 143D in binary?

Figure 4

Problem 4


What is binary 0101 0011 0010 1011 in hexadecimal?

Figure 5

Problem 5


What is binary 1011 1011 1100 0111 in hexadecimal?

Figure 6

Problem 6


What is binary 1000 1100 1001 in hexadecimal?

Figure 7

Practice Problem Answers


Answer 1


Hexadecimal 5E4A is 0101 1110 0100 1010 in binary. Their decimal value is 24,138.

Figure 8

Answer 2


Hexadecimal 5F4 is 0101 1111 0100 in binary. Their decimal value is 1,524.

Figure 9

Answer 3


Hexadecimal 143D is 0001 0100 0011 1101 in binary. Their decimal value is 5,181.

Figure 10

Answer 4


Binary 0101 0011 0010 1011 is 532B in hexadecimal. Their decimal value is 21,291.

Figure 11

Answer 5


Binary 1011 1011 1100 0111 is BBC7 in hexadecimal. Their decimal value is 48,071.

Figure 12

Answer 6


Binary 1000 1100 1001 is 8C9 in hexadecimal. Their decimal value is 2,249.

Figure 13