CSc 3210 Name:
Computer Organization and Programming
Fall 1998
Solutions to Quiz #1 (9 September 1998, Wednesday)
- 1.
- Consider the Floating Point Notation in which 1 bit is used for
Sign, 2 bits for Exponent and 2 bits for Mantissa. Fill in the
real number being represented by the following bit patterns:
| SIGN |
EXPONENT |
MANTISSA |
REAL NUMBER |
| 0 |
00 |
00 |
+0.0000 |
| 0 |
00 |
01 |
+0.0625 |
| 0 |
00 |
10 |
+0.1250 |
| 0 |
00 |
11 |
+0.1875 |
| 0 |
01 |
00 |
+0.0000 |
| 0 |
01 |
01 |
+0.1250 |
| 0 |
01 |
10 |
+0.2500 |
| 0 |
01 |
11 |
+0.3750 |
| 0 |
10 |
00 |
+0.0000 |
| 0 |
10 |
01 |
+0.2500 |
| 0 |
10 |
10 |
+0.5000 |
| 0 |
10 |
11 |
+0.7500 |
| 0 |
11 |
00 |
+0.0000 |
| 0 |
11 |
01 |
+0.5000 |
| 0 |
11 |
10 |
+1.0000 |
| 0 |
11 |
11 |
+1.5000 |
- 2.
- Suppose a machine stores real numbers in floating point notation with
1 bit for sign, 4 bits for exponent and 6 bits for mantissa.
- (a)
- What is the largest number that can be represented in this
notation?
Answer: +126
- (b)
- What is the smallest non-zero positive number that can be
represented in this notation?
Answer: 2-14 = 0.000061035156
- 3.
- Convert the following IEEE floating-point number to decimal notation:
1 10001111 01011101101010000000000
Answer: -89512
Dr. Raj Sunderraman
9/9/1998