Study Sheet - Appendix A/B
Disclaimer: This study sheet covers important terms and concepts that I
found in the text. The absence of a specific item in the text from this list
does not mean that you are not responsible for knowing it. Also,
not valid in Tennessee and for entertainment purposes only.
Appendix A "Binary Numbers"
Terms:
| closure |
radix |
binary |
octal |
| hex |
binary digit (bit) |
|
|
| signed magnitude |
1's complement |
2's complement |
excess 2^(m-1) |
Concepts. You should be able to:
- Explain the impact of finite-precision numbers of closure and other
numeric issues
- Express numbers in binary, octal, hex, and decimal. This includes
converting any number from one base to the other.
- decimal => binary - find the largest power of 2, subtract
and repeat
- decimal => octal - find the largest power of 8, subtract and
repeat... you can also convert to binary and then to octal
- decimal => hex - find the largest power of 16, subtract and
repeat... you can also convert to binary and then to hex
- binary => decimal - sum the value of each binary position
with a value of 1
- binary => octal - combine groups of 3 bits starting at the
point
- binary => hex - combine groups of 4 bits starting at the
point
- octal => decimal - sum the value of each octal position
- octal => binary - expand each octal digit into its 3-bit
value
- octal => hex - convert to binary and then convert to hex
- hex => decimal - sum the value of each hex digit
- hex => binary - expand each hex digit into its 4-bit value
- hex => octal - convert to binary and then convert to octal
- Use the "doubling method" to convert from binary to decimal
- Use the "halving method" to convert from decimal to binary
- Represent a positive or negative number in any of the formats: signed
magnitude, 1's complement, 2's complement, excess 2^(m-1)
- Do binary addition and subtraction with any format
- Do binary multiplication
Appendix B "Floating-point Numbers"
Terms:
| fraction |
mantissa |
exponent |
|
| underflow error |
overflow error |
rounding |
|
| normalized |
significand |
|
|
Concepts. You should be able to:
- Use scientific notation to represent any number
- Explain and use the IEEE floating-point standard 754: single precision (32
bits) and double precision formats (64 bits)
- Express any number in FP 754
- Determine the value of any number encoded in FP 754
- Determine the range of the single or double precision format