1-7
Q8.
What is the MSD and LSD of the following numbers
(a) 420.
(b) 1045.06
(c) 0.0024
(d) 247.0001
Carry and Borrow Principles
Soon after you learned how to count, you were taught how to add and subtract. At that time, you
learned some concepts that you use almost everyday. Those concepts will be reviewed using the decimal
system. They will also be applied to the other number systems you will study.
ADDITIONAddition is a form of counting in which one quantity is added to another. The
following definitions identify the basic terms of addition:
AUGENDThe quantity to which an addend is added
ADDENDA number to be added to a preceding number
SUM The result of an addition (the sum of 5 and 7 is 12)
CARRY A carry is produced when the sum of two or more digits in a vertical column equals or
exceeds the base of the number system in use
How do we handle the carry; that is, the two-digit number generated when a carry is produced? The
lower order digit becomes the sum of the column being added; the higher order digit (the carry) is added
to the next higher order column. For example, let’s add 15 and 7 in the decimal system:
Starting with the first column, we find the sum of 5 and 7 is 12. The 2 becomes the sum of the lower
order column and the 1 (the carry) is added to the upper order column. The sum of the upper order
column is 2. The sum of 15 and 7 is, therefore, 22.
The rules for addition are basically the same regardless of the number system being used. Each
number system, because it has a different number of digits, will have a unique digit addition table. These
addition tables will be described during the discussion of the adding process for each number system.
A decimal addition table is shown in table 1-1. The numbers in row X and column Y may represent
either the addend or the augend. If the numbers in X represent the augend, then the numbers in Y must
represent the addend and vice versa. The sum of X + Y is located at the point in array Z where the
selected X row and Y column intersect.
