Digital Representation
Computers communicate with a binary (on/off) logic system. We can represent
numbers in decimal (base 10), hexadecimal (base 16), or pure binary (base 2).
All binary numbers are represented in big endian format.
- Complete the table below with the other two forms of the given number.
Assume that all values are 8-bit. (2 pts. each, 20 total)
| Decimal |
Hexadecimal |
Binary |
|---|
|
|
0110_0111 |
|
0x0D |
|
| 124 |
|
|
|
|
1111_1111 |
| 256 |
|
|
|
0xDE |
|
|
|
1010_1101 |
| 190 |
|
|
|
|
1010_1010 |
| 85 |
|
|
- What is the largest decimal value that can be represented by an unsigned
8 bit binary value? Please answer is base 10. What about 10, 16, and 24 bits?
(8 pts.)
- What values (two) in the table above would be easy to use as troubleshooting
characters when looking at the signal on an oscilloscope or logic analyzer?
Why? Consider the number and pattern of logic value transitions. What would
be easy to spot? (3 pts.)
- Complete the table below with the unsigned and two’s complement value of
the given binary number. Answers should be base 10 integers.
(2 pts. each, 12 total)
| Binary |
Unsigned Value |
Two’s Complement |
|---|
| 0111_1111 |
|
|
| 1000_0001 |
|
|
| 1111_1110 |
|
|
| 0101_1010 |
|
|
| 0000_0001 |
|
|
| 1000_1100 |
|
|
- Assume a number is stored in the IEEE 754 single-precision floating point
representation. The float is stored in memory as 0x40490E56.
What is the floating point number in decimal form? (5 pts.)
- Why should floating point calculations be avoided, especially in
single-precision systems? (5 pts.)
- How could you implement mathematical operations that involve floating point
math on a resource constrained processor, like an Arduino, without using a
floating point library? (3 pts.)
- What is a common way that complex math like sin, cos, and log are implemented
on resource constrained processors? (3 pts.)