Service manual

STP 11-25R13-SM-TG
Q - 12
(13) Using the short division method, note the conversion of the decimal number 55.
Remainder
2 55
2 27 1
2 13 1
2 6 1
2 3 0
2 1 1
2 0 1
The binary equivalent of decimal 55 = 110111
2
.
(14) Conversion of a large decimal number such as 10050 is accomplished in the same manner.
Remainder
2 10050
2 5025 0
2 2512 1
2 1256 0
2 628 0
2 314 0
2 157 0
2 78 1
2 39 0
2 19 1
2 9 1
2 4 1
2 2 0
2 1 0
2 0 1
Thus, 10050
10
= 10011101000010
2
.
d. Binary Addition
. In adding decimal numbers, the value of any two digits has to be memorized
from a table. Whenever the sum of two digits exceeds the available number symbols, a 1 is carried to the
next-higher-order column. For example: 9 + 1 = 0 with a carry of 1.
(1) In the binary system there are only two symbols, 0 and 1. Hence, adding 1 + 1 in binary
notation exceeds the available number symbols; therefore, the result is 0 with 1 carried to the next-
higher-order column. The rules for binary addition are as follows:
0 1
+1
+1
1 0 (with a carry of 1 to the next column to the left.)
(2) Applying the rules of binary addition, examine the following examples.
Add binary 1010 and 11:
(Carries 1)
1010
+ 11
1101
(3) Converting them to decimal and then adding as shown in this next example can check the sum
of two binary numbers.