# 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

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?

### Problem 2

What is hexadecimal

`5F4`in binary?

### Problem 3

What is hexadecimal

`143D`in binary?

### Problem 4

What is binary

`0101 0011 0010 1011`in hexadecimal?

### Problem 5

What is binary

`1011 1011 1100 0111`in hexadecimal?

### Problem 6

What is binary

`1000 1100 1001`in hexadecimal?

# Practice Problem Answers

### Answer 1

Hexadecimal

`5E4A`is

`0101 1110 0100 1010`in binary. Their decimal value is 24,138.

### Answer 2

Hexadecimal

`5F4`is

`0101 1111 0100`in binary. Their decimal value is 1,524.

### Answer 3

Hexadecimal

`143D`is

`0001 0100 0011 1101`in binary. Their decimal value is 5,181.

### Answer 4

Binary

`0101 0011 0010 1011`is

`532B`in hexadecimal. Their decimal value is 21,291.

### Answer 5

Binary

`1011 1011 1100 0111`is

`BBC7`in hexadecimal. Their decimal value is 48,071.

### Answer 6

Binary

`1000 1100 1001`is

`8C9`in hexadecimal. Their decimal value is 2,249.