Question

CIT 3322 CSC 3322 Computer Architecture

This is designed to comprehensively clarify the number systems. This assignment weights 10 points.

Note:



A cover page with "CIT 3322 CSC 3322, Spring 2019, Assignment #1", your

NAME

, and

your

E-MAIL address

on it.



My preference is typed report. Writing and hand-draw are OK but it should be legible.



Staple if there are more than one sheet.



You can discuss with your classmate, but don't copy.

1. Convert the following decimal numbers to (regular) binary numbers:

a. 99

b. 48.25

2. Convert the following (regular) binary numbers to the decimal numbers:

a. 101010

2

b. 110.10101

2

3. Convert the following negative decimal numbers to binary numbers using three

different kinds of binary representations (sign-magnitude, 1’s complement, and 2’s

complement), respectively:

a. -28

b. -52

4. Convert the following 2’s complement binary numbers to decimal numbers:

a. 010101

b. 101010

5. Covert the following decimal number to BCD code:

a. 49

b. 136

6. Convert the following binary code to gray code:

a. 10101

b. 1010111

7. Convert the following gray code to binary code:

a. 11111

b. 1111100

Answer 1

1 a)1100011

b)110000.01

2. a) 101010 = (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = 42

b)110.10101 = (1 × 2²) + (1 × 2¹) + (0 × 2⁰) + (1 × 2⁻¹) + (0 × 2⁻²) + (1 × 2⁻³) + (0 × 2⁻⁴) + (1 × 2⁻⁵) = 6.65625

3 a) -28=1111111111100100 //binary 2's complement

b) -52=1111111111001100 //binary 2's complement

4 a) 21

b) -22

5) a) 49 = 0100 1001 //In the BCD numbering system, a decimal number is separated into four bits for each decimal digit within the number.

b) 136 = 0001 0011 0110

6) a) 10101=11111

b) 1010111 = 1111100

7) a)10101

b)1010111