Tutorial 1- Numbering system and coding
Dr Rahma Bouaziz A.Y : 2023/2024
PROBLEMS :
1. Express the following decimal numbers in binary:
a. 5,10,20,40,80
b. 3,7,15,31,63
c. 0,1,16,15,64,63,256,255
d. 2n,2n-1,2n+1
2. What is the smallest number and the largest one that can be expressed with
8 bits, 16 bits and 32 bits?
3. What is the binary equivalent of 3.3437510?
4. Do the following conversion problems:
a. (10011010001)2= ()10 f. (100.1111)2= ()10
b. (3527)8= ()10 g. (1.001111)2= ()10
c. (7DA)16= ()10 h. (36.2575)8= ()2= ()16
d. (1011.10101101)2= ()8= ()16 i. (FF.ED)16= ()2= ()8
e. (1111.0010011)2= ()8= ()16
5. Convert to binary, octal and to hexadecimal the decimal number (2023)10
Verify that the binary obtained result is the same obtained by grouping 3 or
4 bits (Octal or Hexadecimal).
6. Give (102.3)5 in base 3.
7. Give (2100122)3 in base 9.
8. What is the decimal equivalent of (11.01011)2?
9. Find the negative decimal number of the sequence 11010111.
10. Represent on 8 bits (-75), (-128) and (-279).
11. Perform the following arithmetic operations:
a. 100100112 +11100102 = ()2 d. 7658 + 4748 = ()16
b. 101101102 - 11000012 = ()2 e. EF2316 – C7A 16 = ()2
c. EE2316 + AB916 = ()8 f. 100102 * 10012 = ()8
g. 10110102 ÷ 10102 = ()2
Digital Logic Design and Computer Architecture
Dr Rahma Bouaziz A.Y : 2023/2024
PROBLEMS :
1. Express the following decimal numbers in binary:
a. 5,10,20,40,80
b. 3,7,15,31,63
c. 0,1,16,15,64,63,256,255
d. 2n,2n-1,2n+1
2. What is the smallest number and the largest one that can be expressed with
8 bits, 16 bits and 32 bits?
3. What is the binary equivalent of 3.3437510?
4. Do the following conversion problems:
a. (10011010001)2= ()10 f. (100.1111)2= ()10
b. (3527)8= ()10 g. (1.001111)2= ()10
c. (7DA)16= ()10 h. (36.2575)8= ()2= ()16
d. (1011.10101101)2= ()8= ()16 i. (FF.ED)16= ()2= ()8
e. (1111.0010011)2= ()8= ()16
5. Convert to binary, octal and to hexadecimal the decimal number (2023)10
Verify that the binary obtained result is the same obtained by grouping 3 or
4 bits (Octal or Hexadecimal).
6. Give (102.3)5 in base 3.
7. Give (2100122)3 in base 9.
8. What is the decimal equivalent of (11.01011)2?
9. Find the negative decimal number of the sequence 11010111.
10. Represent on 8 bits (-75), (-128) and (-279).
11. Perform the following arithmetic operations:
a. 100100112 +11100102 = ()2 d. 7658 + 4748 = ()16
b. 101101102 - 11000012 = ()2 e. EF2316 – C7A 16 = ()2
c. EE2316 + AB916 = ()8 f. 100102 * 10012 = ()8
g. 10110102 ÷ 10102 = ()2
Digital Logic Design and Computer Architecture
