# [#5] – Computer Arithmetic – Questions

As we know that, the use of a smaller base often requires more positions to represent a given value, for example 910 = 10012. Hence, four positions are required instead of one to represent decimal number 9 in binary form. In spite of this, almost all computers use binary numbers.

Information is handled by computer’s electronic/electrical components such as transistors, semiconductors, wires etc, and all these can indicate only two states or conditions – ON (State 1) or OFF (State 0). Transistors are either conducting or non-conducting, magnetic materials are either magnetized in one or opposite direction or non-magnetized, a pulse or voltage is present or absent in wire.

Information is represented within a computer by the presence or absence of these types of signals. Binary number system having only two digits (0 and 1) is most suitable for expressing the two possible states.

Points To Remember:

• Almost all computers use binary numbers for internal computations because electronic circuits for performing arithmetic operations in binary mode can be designed and implemented more easily, reliably, and inexpensively than those required for performing arithmetic operations in decimal mode.
• The rules for binary addition are as follows:
0+0 = 0
0+1 = 1
1+0 = 1
1+1 = 0 plus a carry of 1 to next higher column
• The rules for binary subtraction are as follows:
0-0 =0
0-1 =1 with a borrow from the next column
1-0 =1
1-1 =0
• For a number having n digits, its complement is defined as the difference between the number and the base raised to the nth power minus one.
• A quick way to obtain the complement of a binary number is to transform all its 0s to 1s, and all its 1s to 0s.
• Complementary subtraction is an additive approach of subtraction.
• The rules for binary multiplication are as follows:
0*0 =0
0*1 =0
1*0 =0
1*1= 1
• The rules for binary division are as follows:
0/0 = Divide by zero error
0/1 = 0
1/0 = Divide by zero error
1/1 = 1
• ‘Divide by zero’ is an error condition raised by the computer when any number is divided by zero.
• Most computers use the additive approach for performing subtraction, multiplication, and division operations.

List of Questions

1. Why computers use the binary number system?
2. Add binary numbers 1011 and 101 in both decimal and binary forms.
3. Add binary numbers 1010110 and 1011010.
4. Add binary numbers 10111 and 1011.
5. Find the complement of following numbers:
49510
C16
2910
25
48
324
6. Find the complement of following binary numbers:
10
101
101101
011011
10110001
001101001110
7. Subtract 01101112 from 11011102.
8. Subtract 010102 from 100002.
9. Subtract 0110112 from 1101112.
10. Subtract 2510 from 5010 using complementary method.
11. Subtract 2510 from 2010 using complementary method.
12. Subtract 23410 from 58810 using complementary method.
13. Subtract 21610 from 17210 using complementary method.
14. Subtract 010102 from 100002 using complementary method.
15. Subtract 1101112 from 1011102 using complementary method.
16. Subtract 0110112 from 1101112 using complementary method.
17. Subtract 11112 from 11002 using complementary method.
18. Multiply binary numbers 1100 and 1010.
19. Multiply binary numbers 01101 and 1001.
20. Multiply binary numbers 101111 and 111.
21. Divide 110012 by 1012.
22. Divide 01101112 by 01112.
23. What happens when a number is divided by zero in a computer?
24. Explain how multiplication and division operations are performed in a computer by using additive approach.
25. What is the primary advantage of performing subtraction by complementary method in digital computers?
26. Discuss the advantages and disadvantages of performing various arithmetic operations by additive method in a digital computer.