Binary Number System

Overview

The decimal number system, which is used in daily life, consists of ten numerals: 0123456789. In contrast, the binary number system used by computer hardware consists of two numerals: 0 and 1. This is a direct consequence of a bit consisting of two values. If bits had three values, then the computers would use a number system based on three numerals.

The digits of the decimal system are named incrementally as ones, tens, hundreds, thousands, etc. For example, the number 1023 can be expanded in the following way:

1023 == 1 count of thousand, no hundred, 2 counts of ten, and 3 counts of one

Naturally, moving one digit to the left multiplies the value of that digit by 10: 1, 10, 100, 1000, etc.

When the same rules are applied to a system that has two numerals, we arrive at the binary number system. The digits are named incrementally as ones, twos, fours, eights, etc. In other words, moving one digit to the left would multiply the value of that digit by 2: 1, 2, 4, 8, etc. For example, the binary number 1011 can be expanded as in the following way:

1011 == 1 count of eight, no four, 1 count of two, and 1 count of one

To make it easy to refer to digits, they are numbered from the rightmost digit to the leftmost digit, starting with 0. The following table lists the values of all of the digits of a 32-bit unsigned number in the binary system:

Digit	Value
31	2,147,483,648
30	1,073,741,824
29	536,870,912
28	268,435,456
27	134,217,728
26	67,108,864
25	33,554,432
24	16,777,216
23	8,388,608
22	4,194,304
21	2,097,152
20	1,048,576
19	524,288
18	262,144
17	131,072
16	65,536
15	32,768
14	16,384
13	8,192
12	4,096
11	2,048
10	1,024
9	512
8	256
7	128
6	64
5	32
4	16
3	8
2	4
1	2
0	1