Service manual

STP 11-25R13-SM-TG
Q - 13
1010 10 (8 + 0 + 2 + 0)
+ 11
+3 (2 + 1)
1101
2
13
10
(8 + 4 + 0 + 1)
(4) Another example of binary addition and the conversion is shown.
(Carries 11)
1101 13 (8 + 4 + 0 + 1)
+0110
+6 (0 + 4 + 2 + 0)
10011
2
19
10
(5) Anytime there is a combination of two 1’s, the result is 0 with a carry of 1. When there are
three 1’s in the same column, the result is 1 with a carry of 1. This is illustrated in these two examples.
Add 11
2
and 11
2
: Add 1111
2
and 1011
2
:
(Carries 11) (Carries 1111)
11 1111
+11
+1011
110
2
11010
2
(6) For practice, add the binary numbers. The subscripts are understood to be 2.
(a) 11 (b) 110 (c) 0011 (d) 11011
+01
+10 +101 +1011
(e) 1001 (f) 10101 (g) 111 (h) 111
+111
+1110 + 1 +111
(i) 1110 (j) 101110110
+1111
+ 111001
e. Binary Subtraction
. Subtraction of binary numbers is performed in the same manner as
subtraction of decimal numbers. The rules for binary subtraction are given here:
0 1 1 0
-0
-1 -0 -1
0 0 1 1 with a borrow of 1.
(1) Examine the borrowing process in more detail. Subtracting a binary 1 from 0 is the same as
subtracting a decimal 9 from 0. The borrow of 1, in either case, must come from the next-higher-order
filled column.
(2) A filled column in binary is one that contains a 1. Remember, in binary the next-higher-order
column is always worth twice the value of the former one. Thus, borrowing a 1 from the next-higher-order
column produces two 1’s in the next-higher-order column. When a 1 is subtracted from two 1’s, the result
is 1. Subtracting a binary 1 from a binary 10 in the example following shows this borrowing process.
1
10 Borrowing 1 produces two 1’s (01)
-1
10
-1
1
(3) You should recall from addition that a binary 1 + 1 = 0 with a carry of 1; therefore, a binary 10 is
the same as 1 + 1. Also, a binary 10 is equal to a decimal 2. Thus, you can think of the problem as "two
minus one".