PLease show the answer for 9.5 using the steps used. I already got the correct a

Question

PLease show the answer for 9.5 using the steps used. I already got the correct answer but not entirely sure how?

1001.1 is not the correct answer. I need the normalized format. Give one other example.

For the questions on this page, use a 7-bit floating-point representation that has 4 bits for the significand and 3 bits for the exponent, as shown below. The blue numbers indicate the bit positions of the exponent and significand within this 7-bit format (e.g., bits 6 through 4 are used as the exponent field, bits 3 through 0 are used as the significand field). exponent significand 43 Both the exponent and significand are assumed to be unsigned (there is no sign bit in this format, and the significand has an implicit leading 1. The bias is 0. The value of the representation is therefore given by: 1.significand x 2exponent

Explanation / Answer

9.5
===
A. The integral part = (9)10 = (1001)2
B. Fractional part
0.5 * 2 = 1.0 = Generate 1
  
So, (9.5)10 = (1001.1)=2

C. Add an exponent part :
(1001.1)2 = (1001.1)2 * (2)0
D. Normalize:
(1001.1)2 * (2)0 = (100.11)2 * (2)1
(100.11)2 * (2)1 = (10.011)2 * (2)2
(10.011)2 * (2)3 = (1.0011)2 * (2)4

E. Mantisa = 0011
F. Exponent = 4+(3-4) = 3 = 011 || For the 7-bit the number of bits in exponent = 3

The result is Exponent+Mantisa = 011 0011

5.25
====
A. The integral part = (5)10 = (101)2
B. Fractional part
0.25 * 2 = 0.5 = 0
0.5 * 2 = 1.0 = 1
  
So, (5.25)10 = (101.01)=2

C. Add an exponent part :
(101.01)2 = (101.01)2 * (2)0
D. Normalize:
(101.01)2 * (2)0 = (10.101)2 * (2)1
(10.101)2 * (2)1 = (1.0101)2 * (2)2

E. Mantisa = 0110
F. Exponent = 2+(3-2) = 3 = 011 || For the 7-bit the number of bits in exponent = 3

The result is Exponent+Mantisa = 011 0110

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.