B.6. Negative Binary Numbers: Twos Complement Notation
Answers to Self Review Exercises
B.1 |
a) 10, 2, 8, 16. b) 1 (the base raised to the zero power). c) The base of the number system. |
||||||||||||||||||||
B.2 |
a) False. Hexadecimal does this. b) False. The highest digit in any base is one less than the base. c) False. The lowest digit in any base is zero. |
||||||||||||||||||||
B.3 |
Fewer. |
||||||||||||||||||||
B.4 |
Hexadecimal. |
||||||||||||||||||||
B.5 |
Fill in the missing values in this chart of positional values for the rightmost four positions in each of the indicated number systems:
|
||||||||||||||||||||
B.6 |
Octal 6530; Hexadecimal D58. |
||||||||||||||||||||
B.7 |
Binary 1111 1010 1100 1110. |
||||||||||||||||||||
B.8 |
Binary 111 011 001 110. |
||||||||||||||||||||
B.9 |
Binary 0 100 111 111 101 100; Octal 47754. |
||||||||||||||||||||
B.10 |
Decimal 2+4+8+32+64=110. |
||||||||||||||||||||
B.11 |
Decimal 7+1*8+3*64=7+8+192=207. |
||||||||||||||||||||
B.12 |
Decimal 4+13*16+15*256+14*4096=61396. |
||||||||||||||||||||
B.13 |
Decimal 177 to binary: 256 128 64 32 16 8 4 2 1 128 64 32 16 8 4 2 1 (1*128)+(0*64)+(1*32)+(1*16)+(0*8)+(0*4)+(0*2)+(1*1) 10110001 to octal: 512 64 8 1 64 8 1 (2*64)+(6*8)+(1*1) 261 to hexadecimal: 256 16 1 16 1 (11*16)+(1*1) (B*16)+(1*1) B1 |
||||||||||||||||||||
B.14 |
Binary: 512 256 128 64 32 16 8 4 2 1 256 128 64 32 16 8 4 2 1 (1*256)+(1*128)+(0*64)+(1*32)+(0*16)+(0*8)+(0*4)+(0*2)+(1*1) 110100001 One's complement: 001011110 Two's complement: 001011111 Check: Original binary number + its two's complement 110100001 001011111 --------- 000000000 |
||||||||||||||||||||
B.15 |
Zero. |
Appendix C Using the Visual Studio 2005 Debugger
|