Service manual

STP 11-25R13-SM-TG
Q - 9
(5) Since each place to the left of the decimal point represents a power of 10, see in this example how
the number 42,337 can be written using powers of 10.
4 x 10
4
= 40,000
2 x 10
3
= 2,000
3 x 10
2
= 300
3 x 10
1
= 30
7 x 10
0
= 7
42,337 Total
(6) Many students make a common error when they count the number of digits to the left of the
decimal point, and give that digit a power equal to the number of places counted. This error results
because they forget that the first
digit (or place) always carries a power of zero, regardless of the number
system used. Do not get places
and place value confused. For example, decimal number 1001 has four
digits, but the fourth place digit has a place value of "ten to the third", not "ten to the fourth". It is
important that you understand place value in relation to the power of the base number. You will use this
concept in the number systems that follow.
c. The Binary System
(Conversion). The binary number system (base 2) requires only two
symbols: 0 and 1. Any number, regardless of how large, can be written using these two symbols. A
digital circuit using this system requires only two voltage levels to represent a 0 or a 1, which greatly
simplifies computer circuits.
(1) A typical binary number looks like this, 1011010. Each digit, 0 or 1, is often referred to as a bit
,
which is simply short for binary digit. The binary number 1011010 contains seven bits.
(2) A binary number such as 101 is read as "one, zero, one," not "one hundred and one". For this
reason, it is written as 101
2
. The place value of a bit is expressed in powers of two, which is shown in
Table Q-8. This table also shows the decimal value of each power of two. Note that the decimal value
doubles for each increasing power of two.
Table Q-8. Powers of Two
(3) Using powers of two, follow the procedure outlined here for converting a binary number to a
decimal number.
(a) Start with the first bit to the left of the decimal (final) point.
(b) Multiply the bit by its place value.
(c) Multiply each remaining bit by its place value. (A zero bit times its place value always equals
zero; it acts as a placeholder.)
Power of 2 Decimal Equivalent
2
10
1024
2
9
512
2
8
256
2
6
64
2
5
32
2
4
16
2
3
8
2
2
2
2
0
1