Hexadecimal (base 16) notation for memory addresses

A binary digit or bit is a 0 or a 1. Thus a bit has one of two possible values.
A series of 8 bits is called a byte. For example, 01010101.
A series of 4 bits is called a nibble. For example, 0101.

A computer’s memory is a series of containers called cells. Each cell holds one byte.

Each cell has an identifying number, called its memory address.
On our machine storm.cis.fordham.edu, a memory address is conventionally written in hexadecimal notation.
That’s why the number 9 in the following diagram is followed by A and B instead of by 10 and 11.

On our machine, a C++ value of data type int occupies 32 bits of memory, so we use four consecutive cells to hold it.
For example, the memory in the diagram uses cells number 4 through 7 inclusive to hold the 32-bit int value 2025.

	int i {2025};

Let’s see how to write a number in binary (base 2) and hexadecimal (base 16).

The digits of a number (2025) written in decimal (base 10)

Each place has 10 times the value of the previous one.
Depending on the number, we might need to write ten decial digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

2 × 1000 = 2000
0 ×  100 =    0
2 ×   10 =   20
5 ×    1 =    5
           2025

The digits of the same number (2025), written in binary (base 2)

Each place has 2 times the value of the previous one.
The only binary digits we will ever need to write are 0 and 1.

1 × 1024 = 1024
1 ×  512 =  512
1 ×  256 =  256
1 ×  128 =  128
1 ×   64 =   64
1 ×   32 =   32
0 ×   16 =    0
1 ×    8 =    8
0 ×    4 =    0
0 ×    2 =    0
1 ×    1 =    1
           2025

Our number 2025 consists of a series of 11 bits when written in binary.
We will usually consider bits in groups of 4 or 8 at a time, so let’s expand our 11-bit number to 16 bits by adding 5 leading 0’s.
Now our number 2025 consists of 2 complete bytes, because 2 = 16/8.

0 × 32768 =    0
0 × 16384 =    0
0 ×  8192 =    0
0 ×  4096 =    0
0 ×  2048 =    0
1 ×  1024 = 1024
1 ×   512 =  512
1 ×   256 =  256
1 ×   128 =  128
1 ×    64 =   64
1 ×    32 =   32
0 ×    16 =    0
1 ×     8 =    8
0 ×     4 =    0
0 ×     2 =    0
1 ×     1 =    1
            2025

Abbreviate the 16 bits with 4 hex digits.

As we just saw, writing the value of a number in binary usually takes many bits. That’s why they invented hexadecimal digits. Each hexadecimal digit (hex digit) stands for a series of 4 binary digits (bits). In other words, each hex digit stands for 1 nibble.

Here are the 16 nibbles that the 16 hex digits stand for.

We can now write out 16-bit number (2025 = 0000011111101001) with only 4 hex digits (07E9):

Conversion programs

Type control-d into the first two programs to signal that you’re done typing.

1. dectohex.C: convert base 10 to base 16.
2. hextodec.C: convert base 16 to base 10.
3. table.C: decimal (base 10) and hexadecimal (base 16), side by side.