number_system

# 2 the rules for binary addition are as follows 000

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: ers for internal computations because electronic circuits for performing arithmetic operations in binary mode can be designed and implemented more easily and reliably at a much lesser cost than those required for performing arithmetic operations in decimal mode. 2. 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 3. The rules for binary subtraction are as follows: 0-0=0 1-0=1 1-1=0 0 - 1 = 1 with a borrow from the next column 4. For a number, which has n digits in it, a complement is defined as the difference between the number and the base raised to the nth power minus one. 5. A quick way to obtain the complement of a binary number is to transform all its 0s to Is, and all its Is to 0s. 6. Complementary subtraction is an additive approach of subtraction. 7. The rules for binary multiplication are as follows: 0x0=0 0x1=0 1x0=0 1x1=1 8. The rules for binary division are as follows: 0÷1=0 1÷1=1 9. Most computers use the additive approach for performing multiplication and division operations. Questions 1. 2. 3. 4. 5. (a) (b) (c) 6. (a) (b) (c) 7. 8. 9. Why have computers been designed to use the binary number system? Add the binary numbers 1011 and 101 in both decimal and binary form. Add the binary numbers 1010110 and 1011010. Add the binary numbers 10111 and 1011. Find the complement of the following numbers: 49510 (d) C16 2910 (e) 25 48 (f) 324 Find the complement of the following binary numbers: 10 (d) 011011 101 (e) 10110001 101101 (f) 001101001110 Subtract 01101112 from 11011102. Subtract 010102 from 100002. 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...
View Full Document

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

Ask a homework question - tutors are online