number_system

# The second step is simply to subtract the lower value

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the column to the left. It is important to note here that the value borrowed depends upon the base of the number and is always the decimal equivalent of the base. Thus, in decimal, 10 is borrowed; in binary, 2 is borrowed; in octal, 8 is borrowed; in hexadecimal, 16 is borrowed. The second step is simply to subtract the lower value from the upper value. The complete table for binary subtraction is as follows:64 0-0=0 1-0=1 1-1=0 0 - 1 = 1 with a borrow from the next column . Observe that the only case in which it is necessary to borrow is when 1 is subtracted from 0. The exact procedure is illustrated with the examples given below. Example 5.4. Subtract 011102froml01012 Solution: Borrow 12 0202 10101 -01110 00111 In the first column, 0 is subtracted from 1. No borrow is required in this case and the result is 1. In the second column, we have to subtract 1 from 0. As seen in the table for binary subtraction, a borrow is necessary to perform this subtraction. Hence, a 1 is borrowed from the third column, which becomes 2 in the second column because the base is 2. A 1 in the 4s column is equal to 2 in the 2s column. Now, in the second column, we subtract 1 from 2 giving a result of 1. The borrow performed in the second column reduces the 1 in the third column to 0. Hence, in the third column, once again we have to subtract 1 from 0 for which borrow is required. The fourth column contains a 0 and thus has nothing to borrow. Therefore, we have to borrow from the fifth column. Borrowing 1 from the fifth column gives 2 in the fourth column. A 1 in the 16s column equals 2 in the 8s column. Now the fourth column has something to borrow. When 1 of the 2 in the fourth column is borrowed, it becomes 2 in the third column. Now, in the third column, we subtract 1 from 2 giving a result of 1. The borrow performed in the third column reduces the 1 in the fifth column to 0 and the 2 in the fourth column to 1. Hence, subtraction of the fourth column is now 1 from 1, giving 0 and in the fifth column, subtraction is 0 from 0, giving 0. Thus the final result of subtraction is 00111 2. The result may be verified by subtracti...
View Full Document

## This document was uploaded on 04/07/2014.

Ask a homework question - tutors are online