Hex, Binary, and Decimal Additional LearningΒΆ

Note: This is the additional learning section of the Hex, Binary, and Decimal tutorial, the original tutorial is available here.

Ok, so let’s visit our previous practice problems. We’ll walk through them step by step.

Decimal Hexadecimal Binary
10 ? ?
72 $48 ?
? ? 101011
? $1E ?

Ok, so for the first problem, we need to convert 10 in decimal to hexadecimal. Let’s make another chart.

Place 16384’s 256’s 16’s 1’s
Digit 0 0 0 10

Since we have 10 1’s, no 16’s, 256’s, or 16384’s, our number is still 10 in hexadecimal.

Decimal Hexadecimal Binary
10 10 ?

Great! Now we need to convert 10 to binary.

How many 16’s go into 10? Zero.

Place 16’s 8’s 4’s 2’s 1’s
Digit 0        

How many 8’s go into 10? One. Now we subtract 8 from 10, and are left with 2.

Place 16’s 8’s 4’s 2’s 1’s
Digit 0 1      

How many 4’s go into 2? None.

Place 16’s 8’s 4’s 2’s 1’s
Digit 0 1 0    

How many 2’s go into 2? One. 2-2=0, so we are done

Place 16’s 8’s 4’s 2’s 1’s
Digit 0 1 0 1 0

10 in binary is 01010

Decimal Hexadecimal Binary
10 10 01010

Ok, so now for the next problem, we are given two values, and we need to solve for the binary form.

Decimal Hexadecimal Binary
72 $48 ?

But which way is easiest to solve from?

We can convert decimal to binary like so:

Place 64’s 32’s 16’s 8’s 4’s 2’s 1’s
Digit 1 0 0 ? ? ? ?

72-64= 8

Place 64’s 32’s 16’s 8’s 4’s 2’s 1’s
Digit 1 0 0 1 0 0 0

8-8=0

72 in binary is 1001000

Decimal Hexadecimal Binary
72 $48 1001000

But what if we want to convert directly from hexadecimal to binary?

$48 in hexadecimal = (4*16 2 ) * (8 * 16)

$48 in hexadecimal = (1*2 6 ) * (1*2 3 )

Another way of writing the chart is with powers of 2

Place 6 5 4 3 2 1 0
Digit 1 0 0 1 0 0 0

But you can still also do

Place 64’s 32’s 16’s 8’s 4’s 2’s 1’s
Digit 1 0 0 1 0 0 0

$48 = (64) * (8)

You still get the same answer, 1001000

Ok, now for the next problem, we need to convert binary back in to decimal and hexadecimal. Once again, we can either decide to convert binary to decimal and then to hexadecimal or to convert to each using binary.

Decimal Hexadecimal Binary
? ? 101011

Since we already know how to convert decimal to hexadecimal, we’re going to convert directly to each.

Decimal:

Place 32’s 16’s 8’s 4’s 2’s 1’s
Digit 1 0 1 0 1 1

%101011 to decimal = (1*32) + (0 * 16) + (1*8) + (0*4) + (1*2) + (1*1) %101011 to decimal = 43

Decimal Hexadecimal Binary
43 ? 101011

Once again, %101011 = (1*32) + (0 * 16) + (1*8) + (0*4) + (1*2) + (1*1) 32 is 2 *16, or 2 16’s. Since there are no other 16’s that can fit inside, we put 2 in the 16’s column.

Place 16’s 1’s
Digit 2 ?

How many do we have left over? 1*8, 1*2, and 1*1. In Hexadecimal, we have B left over.

Place 16’s 1’s
Digit 2 B

So our hexadecimal version of %101011 is 2B

Decimal Hexadecimal Binary
43 2B 101011

Try the final one on your own, if you get stuck, our work is below. You can also check your answer when you are finished.

Decimal Hexadecimal Binary
? $1E ?

The solution:

Decimal Hexadecimal Binary
? $1E ?
Decimal Hexadecimal
10 A
11 B
12 C
13 D
14 E
15 F

E is 14 in decimal.

$1E in decimal = (1*16 1 ) * (14*16 0 )

$1E = 30 in decimal

Decimal Hexadecimal Binary
30 $1E ?

$1E in decimal = (1*16 1 ) * (14*16 0 )

Place 32’s 16’s 8’s 4’s 2’s 1’s
Digit 0 1 ? ? ? ?

(14*16 0 )

14=8+4+2

Place 32’s 16’s 8’s 4’s 2’s 1’s
Digit 0 1 1 1 1 0
Decimal Hexadecimal Binary
30 $1E 011110

Oh, and one last thing, now that we have learned to convert between these three systems ourselves, here is a cheatsheet:

Decimal Hexadecimal Binary
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111

You can use it to convert easily, for example: $7F in binary is 01111111

If you still don’t understand, you can ask around on the Cemetech forums. These concepts will be used quite frequently, so you need to master them.

To the next tutorial!