Since 1 is the largest digit in the binary number

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s, the addition table for binary arithmetic is very simple consisting of only four entries. The complete table for binary addition is as follows: 0+0=0 0+1=1 1+0=1 1 + 1=0 plus a carry of 1 to next higher column Carry-overs are performed in the same manner as in decimal arithmetic. Since 1 is the largest digit in the binary number system, any sum greater than 1 requires that a digit be carried over. For instance, 10 plus 10 binary requires the addition of two 1 's in the second position. Since 1 + 1=0 plus a carry-over of 1, the sum of 10 + 10 is 100 in binary. By repeated use of the above rules, any two binary numbers can be added together by adding two bits at a time. The exact procedure is illustrated with the examples given below. Example 5.1. Add the binary numbers 101 and 10 in both decimal and binary form. Solution: Binary - Decimal 101 5 +10 +2 111 7 Add the binary numbers 10011and 1001 in both decimal and binary form. Solution: Binary Carry 11 10011 +1001 11100 Decimal Carry 1 19 +9 28 In this example of binary addition, a carry is generated for first and second columns. Example 5.3. Add the binary numbers 100111 and 11011 in both decimal and binary form. Solution: Binary Decimal Carry 11111 carry 1 100111 39 +11011 +27 1000010 66 In this example, we face a new situation (1 + 1 + 1) brought about by the carry-over of 1 in the second column. This can also be handled using the same four rules for binary addition. The addition of three 1 's can be broken up into two steps. First we add only two 1 's giving 10(1 + 1 = 10). The third 1 is now added to this result to obtain 11 (a 1 sum with a 1 carry). So we conclude that 1 + 1 + 1 = 1 plus a carry of 1 to next higher column. Subtraction The principles of decimal subtraction can as well be applied to subtraction of numbers in other bases. It consists of two steps, which are repeated for each column of the numbers. The first step is to determine if it is necessary to borrow. If the subtrahend (the lower digit) is larger than the minuend (the upper digit), it is necessary to borrow from...
View Full Document

This document was uploaded on 04/07/2014.

Ask a homework question - tutors are online