BINARY NUMBER SYSTEM
The binary number system is a system that uses only the digits 0 and 1 as codes. All other digits (2 to 9) are thrown away.
... [Show More]
To represent decimal numbers and letters of the alphabet with the binary code, you have to use different strings of binary digits number for each or letter. The idea is similar to the Morse code, where strings of dots and dashes are used to code all numbers and letters. What follows is a discussion of decimal and binary counting.
Decimal Odometer
To understand how to count with binary numbers, it helps to review how an odometer (miles indicator of a car) counts with decimal numbers.
When a car is new, its odometer starts with00000 After 1 km the reading becomes 00001
Successive kms produce 00002, 00003, and so on, up to 00009
A familiar thing happens at the end of the tenth km. When the units wheel turns from 9 back to 0, a tab on this wheel forces the tens wheel to advance by 1. This is why the numbers change to00010
Reset-and-Carry
The units wheel has reset to 0 and sent a carry to the tens wheel. Let's call this familiar action reset and carry The other wheels of an odometer also reset and carry. For instance, after 999 kms the odometer shows 00999
What does the next km do? The units wheel resets and carries, the tens wheel resets and carries, the hundreds wheel resets and carries, and the thousands wheel advances by 1, to get 01000
Binary Odometer
Visualize a binary odometer as a device whose wheels have only two digits, 0 and 1. When each wheel turns, it displays 0, then 1, then back to 0, and the cycle repeats. A four-digit binary odometer starts with
0000 (zero)
After 1 mile, it indicates
0001 (one)
The next mile forces the units wheel to reset and carry, so the numbers change to
0010 (two)
The third mile results in 0011 (three)
After 4 miles, the units wheel resets and carries, the second wheel resets d carries, an [Show Less]