KNOWARE
Software for Education and Industry
Because each bit or transistor of a computer can only be on or off, computers are based on the binary numbering system. Binary means 2. There are two digits, 0 and 1, corresponding to a bit or transistor being on or off. But just like in the decimal numbering system, each digit has place value. Here's how it works:Decimal System:Place Value: 10^{3}=1000 10^{2}=100 10^{1}=10 10^{0}=1
Digit: X X X X.
Example: 3 6 5 9 = 3x1000 + 6x100 + 5x10 +9x1 = 3,659
Binary System:
Place Value: 2^{4}=16 2^{3}=8 2^{2}=4 2^{1}=2 2^{0}=1Digit: X X X X X.
Example 1: 1 0 1 1 0 = 16+4+2=22 in base 10 (decimal)
Example 2: 1 1 1 1 0 = 16+8+4+2=30 in base 10 (decimal)
Example 3: 0 0 0 1 1 = 2+1=3 in base 10 (decimal)
So, since there are only 2 digits in a
computer (1 and 0), the decimal number 22 would be represented by
101110 in a computer, the decimal number 30 would be represented
by 11110 in a computer, and the decimal number 3,659 would be
represented by 111001001011 in a computer.
So now, decimal number 22 equals hex number 16, decimal number 30 equals hex number 1E, and decimal number 3,659 equals hex number E4B. Since decimal numbers 0 through 9 look the same as hex numbers 0 through 9, hex numbers are often written with a leading $ sign, the letter H, or the word hex. For example: $16, H16, 16H, or hex 16 all mean the hex number 16, not the decimal number 16.Hexadecimal System:
Place Value: 16^{3}=4,096 16^{2}=256 16^{1}=16 16^{0}=1Digit: X X X X.
Example 1: 3 6 5 9 = 3x4,096 + 6x256 + 5x16 + 9x1 = 13,913
Example 2: 0 0 C F = 12x16 + 15x1 = 207
Example 3: 0 1 0 0 = 1x256 = 256
Figure 4.3 Equivalent Decimal, Binary, and Hexadecimal Numbers
Decimal Number |
Binary |
Hexadecimal |
0 |
0 |
0 |
1 |
1 |
1 |
2 |
10 |
2 |
3 |
11 |
3 |
4 |
100 |
4 |
5 |
101 |
5 |
6 |
110 |
6 |
7 |
111 |
7 |
8 |
1000 |
8 |
9 |
1001 |
9 |
10 |
1010 |
A |
11 |
1011 |
B |
12 |
1100 |
C |
13 |
1101 |
D |
14 |
1110 |
E |
15 |
1111 |
F |
16 |
10000 |
10 |
17 |
10001 |
11 |
18 |
10010 |
12 |
19 |
10011 |
13 |
How Microprocessors Work is written in .html format so you
can use your favorite internet browser to navigate through it
using hyperlinks, bookmarks, and word searches. How
Microprocessors Work requires no software installation on
your computer. Just double-click on Table
of Contents.html.
How Microprocessors Work is written by a Professional Engineer with 14 years industrial experience and 20 years experience teaching electrical engineering technology at the college level.
Hardware/Software Requirements:
An internet browser such as Internet Explorer^{®}, Netscape^{®}, Firefox^{®}, Chrome^{®}, etc.