**ENEE
244 (01**). Spring 2006 **

**Homework
1**

*Due back in class on Friday, Feb 10.*

1. Convert the following binary numbers to decimal: (a) 1101; (b) 10111001.

2. Convert the following decimal numbers to binary: (a) 23; (b) 498.

3. Convert the following numbers to
decimal: (a) (34)_{7}; (b) (76)_{8}.

4. Convert
(a) (47)_{10} to radix 8; (b) (63)_{10} to base 16.

5. Convert (a) (11010110111)_{2} to hexadecimal; (b) (4532)_{8}
to binary.

6. Convert the following decimal numbers to binary: (a) 0.75; (b) 5.3.

7. Add the binary numbers (a) 0101 and 1001; (b) 01101.01 and 1001011.101.

8. Do the following subtractions: (a) 1100 - 1001; (b) 101101 - 11010.

9. Multiply: 10100×101.

10. Find the diminished radix complement of
(a) (76)_{8}; (b) (10010)_{2}.

11. Find the radix complement of (445)_{10}.

12. Represent the following binary numbers in an 8-bit signed-magnitude scheme: (a) +1001; (b) -1011.

13.
A 6-bit computer uses the signed 2's complement representation. It adds 10011 + 11101. State the answer. How is the
overflow detected? */* Hint: In such a representation,
negative numbers are stored as 2's complement of their absolute value. Positive
numbers are represented just like in the sign-magnitude scheme. */*

14. An 8-bit computer uses the signed 2's
complement representation. Show how this computer performs (a) 111010 -
1100; (b) 101 - 10110. * *

15. A 7-bit computer uses the signed 2's complement representation. What is the range of integers that can be represented in this scheme?