1. Architecture and Logic Gates
Al-Mamoon University College Computer Science Department Second Year
Architecture and Logic Gates
Number System
By Dr.Mazin Alzewary

2. Number System Converter
Digital Logic
Digital logic is the field that is used as main building components for the most digital devices Mostly we have
Logic 0 (low) 0 volt Logic 1(high) +5 volt
Number System
System
Base
Symbols
Decimal 10
0, 1, … 9
Binary 2
0, 1
Octal 8
0, 1, … 7
Hexa-decimal 16
0, 1, … 9, A, B, … F
Number System Converter
Q ) Convert to decimal number
Q) Convert 724 octal to decimal number
Q) Convert ABC hexa to decimal number

3. Q) Convert 125 decimal to binary number
Q) Convert 705 octal to binary number
Q) Convert 10AF hexa to binary number
Q) Convert 4321 decimal to octal number

4. Q) Convert 4321 decimal to hexa number
Q) Convert binary to octal number
Q) Convert binary to hexa number
Q) Convert 1076 octal to hexa number

5. Q) Convert 1F0C hexa to octal number

7. Binary Addition
Binary Subtraction
Binary Multiplication

8. Binary Division
Step 0
Does 11 go into 1? No, because it’s greater than 1. Does 11 go into 10? No, because it’s greater than
10. Does 11 go into 101? Yes, because it’s less than or equal to 101. (Remember, these are binary numerals; pronounce them “one-one”, “one-zero”, “one-zero-one”, etc.)
Step 1
Divide: Does 11 go into 101? (Yes, we already know that from step 0.) How many times does it go in? One time. There is no guessing. It’s easy to see 11 is less than 101, so we know it goes in. And if it goes in, it goes in only once.
Multiply: 1 x 11 = 11. (Remember how simple it is to “multiply” a binary number by a single digit — just copy the number down if that single digit is 1, or write down 0 if that single digit is 0.)
3. Subtract: 101 – 11 = 10.
4. Bring down: Bring down the 1 to make 101.

9. Step 2
Divide: Does 11 go into 101? Yes, 1 time.
Multiply: 1 x 11 = 11.
3. Subtract: 101 – 11 = 10.
4. Bring down: Bring down the 1 to make 101.
Step 3
Step 4
4. Bring down: Bring down the 0 to make 100.
Step 5
Divide: Does 11 go into 100? Yes, 1 time.
3. Subtract: 100 – 11 = 1.
4. Bring down: Bring down the 0 to make 10.
Step 6
Divide: Does 11 go into 10? No (write down a 0).
Multiply: (We don’t need to record this step; we’re just going to get 0.)
Subtract: (We don’t need to record this step; we’re just going to get 10.)
Bring down: Bring down the 0 to make 100.
Step 7
We stop here, recognizing that we divided 100 by 11 two steps ago. This means we have a two-digit cycle (10) from here on out. The quotient is

10. Questions Q1) Convert the number (123)10 to binary number
Q2) Convert the number to hexadecimal number Q3) Convert the number to octal number
Q4) Convert the number (167)10 to hexa number Q5) Convert the number (345)8 to hexadecimal Q6) Convert the number (FA12)16 to octal number
Q7) Convert the number (DF3)16 to decimal number Q8) Convert the number (786)8 to hexadecimal
Q9) What is result of (1233)10- (342)10
Q10) What is result of (1233)10- (342)8
Q11) What is result of Q12)What is result of Q13)What is result of Q14)What is result of Q15)What is result of Q16)What is result of Q17)What is result of
( )10- (342)16
(101110)2- (1101)2
(101110)2 + (11101)2
(1011)2 * (1101)2
(101110)2 / (1101)2
(101.11)2- (11.01)2
( )2 + (110.1)2
Q18) Convert the number (78.6)8 to hexadecimal Q19) Convert the number (32.4)10 to octal
Q20) What is the result of (97.86)10 * (32.4)10 to hexadecimal