digital logic

ECE 204 Introduction to Digital Logic Bill Nelson Homework #1

01/09/17 1 Winter, 2017

NAME: ______________________________________ Due: 1/18/2017 Show your work. Answers without supporting work will not earn full credit. When evaluating fractional numbers (i.e. numbers less than one), truncate at four digits: 0.nnnn. You may use a calculator but you must still record your intermediate results. 1. Give the general expression for a positional number in base r of (n+1)

Integer digits and m fractional digits. (Recall weights of an (n+1) digit integer are numbered from n to zero.)

2. Convert the following hexadecimal numbers to octal using binary

as the intermediary: a. (17F.2A59)16 : b. (2B.36EF)16 : c. (DEAF.ED)16 :

ECE 204 Introduction to Digital Logic Bill Nelson Homework #1

01/09/17 2 Winter, 2017

2. Convert the following octal numbers to hexadecimal using binary

as the intermediary: a. (476.225)8 : b. (5123.357)8 : c. (5655.6655)8 :

3. Express the following in one’s complement format using 8 bits: a. (‒27)8 : b. ‒(1)10 :

ECE 204 Introduction to Digital Logic Bill Nelson Homework #1

01/09/17 3 Winter, 2017

PROBLEM #3 Continued:

c. ‒(1011.101)2 : d. (6 7/8)10 : e. (‒010.1010)2 :

4. Express the following in nine’s complement format using 8 digits: a. (‒884.631)10 : b. ‒(3407.28)10 :

ECE 204 Introduction to Digital Logic Bill Nelson Homework #1

01/09/17 4 Winter, 2017

PROBLEM #4 Continued:

c. ‒(120.485)10 : d. (‒61.8267)10 : e. (‒5976.08)10 :

5. Express the following in two's complement format using 8 bits: a. ‒(1)10 : b. (‒5.3)16 :

ECE 204 Introduction to Digital Logic Bill Nelson Homework #1

01/09/17 5 Winter, 2017

PROBLEM #5 Continued:

c. (‒111.001)2 : d. (‒1011.110)2 : e. (5A)16 :

6. Express the following in sign-magnitude format using 8 bits or 8 digits as appropriate: a. (‒2701.43)10 : b. (‒FC4B.6)16 :

ECE 204 Introduction to Digital Logic Bill Nelson Homework #1

01/09/17 6 Winter, 2017

PROBLEM #6 Continued:

c. (‒11 100.1)2 : d. (4423.012)5 : e. (0.654 32)8 :

7. Express the following as 6 digit decimal numbers in binary coded

decimal (BCD) format: a. (380.27)10 : b. (‒92.55)10 :

ECE 204 Introduction to Digital Logic Bill Nelson Homework #1

01/09/17 7 Winter, 2017

PROBLEM #7 Continued:

c. (‒867.09)10 :

8. Express the following as 6 digit decimal numbers in excess three

(XS-3) format: a. (‒1.3872)10 : b. (‒901.56)10 : c. (987.12)10 :

ECE 204 Introduction to Digital Logic Bill Nelson Homework #1

01/09/17 8 Winter, 2017

9. Convert from the indicated base to decimal. Truncate fractional

numbers to 4 digits: a. (5314.24)6 : b. (3412.03)5 : c. (3B7C.14)13 :

ECE 204 Introduction to Digital Logic Bill Nelson Homework #1

01/09/17 9 Winter, 2017

10. Convert from decimal to the indicated base. Truncate fractional

numbers to 4 digits: a. (2989.71)10 to base 16: b. (5423.15)10 to base 6: c. (238.36)10 to base 11: