PC Hardware A Beginner’s Guide

9. 9 divided by 2 equals 4 with a remainder of 1


10. 4 divided by 2 equals 2 with a remainder of 0


11. 2 divided by 2 equals 1 with a remainder of 0


12. 1 divided by 2 equals 0 with a remainder of 1

If you now record the remainders beginning with ste p1 and the remainder of each

ste pto the left of the first one, you will get the binary value of 100110100101 or 2,469. If

you want to verify this, use the Windows Calculator in its Scientific view. Click on the

Dec button and enter the decimal value, then click on the Bin button to display the binary

equivalent. I guess that’s an even easier way to convert a binary number, isn’t it?

Just for Fun

Some of the other names used for other binary words are listed in Table 3-2.

Binary Logic Operations

Processors use binary numbers for addressing, arithmetic, and to make comparisons, such as

equal to, less than, greater than, not equal to, not less than, or not greater than. Beyond

addressing (see Chapter 7) and arithmetic, a processor performs logical (comparison) and

data shift operations using three functions: AND, OR, and EXCLUSIVE OR. These three bi-

naryfunctionsareapartofBooleanalgebra,whichisusedtotesttwovaluestoproduceathird.

AND Operations

TheANDBoolean(pronouncedboo-lee-un)algebraoperationhasaverysimplesetofrules:

 Only two truths equal a truth

 A false always makes a false

(^44) PC Hardware: A Beginner’s Guide
Size Name(s)
2 bits Crumb or tayste
5 bits Nickel
10 bits Deckel
16 bits Playte or chawmp
32 bits Dynner
48 bits Gawble
Table 3-2. Other Binary Words