💻
Fundamentals of C.S, Made by Haneen
Created @October 7, 2023 9:01 PM
Class Computer Science
Type Lecture
Reviewed
Number systems:
Decimal number system:
💡 BASE: 10 SYMBOLS: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
To represent the number (234)10: 2*10(2) + 3*10(1) + 4*10(0) = 200 + 30 + 4 = 234
The 2 lies in the Hundredth place / The 3 lies in the tenth place. / The 4 lies in the unit.
Decimal to binary:
, 💡 BASE: 2 SYMBOLS: 0, 1 1 BYTE = 8 BITS 1 BIT can
2 BITS can store one of these 4 options: 00/ 01/ 10/11 (like a probability or as in 2 to the pow
3 BITS can store three of 8 options (2 to the power of three)
Binary to decimal:
The number (1001)2 in binary can be explained as: 1*2(3) + 0*2(2) + 0*2(1) + 1*2(0) = 8+
Where the 1*2(3) is the most significant bit (MSB). The 1*2(0) is the least sig
Fractional conversion:
(0101.011)2 = two parts: a real part / fraction
Real part = 0101 = 0*2(3) + 1*2(2) + 0*2(1) + 1*2(0) = 4 + 1 = (5)10
Fraction = 0.011 = 0*2(-1) + 1*2(-2) + 1*2(-3) = 0.125 + 0.25 = 0.375
Binary to octal:
When converting to octal, always start with binary.
(100001)2 = divide into three-digit parts starting from right:
421 421
100 001
4 1
لو الرقم تحته واحد بجمع الي فوق
Then the number in octal will be (41)8
Binary to Hexadecimal:
(100001)2 in binary to hexadecimal is the number (21)16.
Divide to four-digit parts starting from right: (if there are no numbers enough add zeros)
8421 8421
0010 0001
2 1
Octal number system:
💡 BASE: 8 SYMBOLS: 0, 1, 2, 3, 4, 5, 6, 7.
Fundamentals of C.S, Made by Haneen
Created @October 7, 2023 9:01 PM
Class Computer Science
Type Lecture
Reviewed
Number systems:
Decimal number system:
💡 BASE: 10 SYMBOLS: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
To represent the number (234)10: 2*10(2) + 3*10(1) + 4*10(0) = 200 + 30 + 4 = 234
The 2 lies in the Hundredth place / The 3 lies in the tenth place. / The 4 lies in the unit.
Decimal to binary:
, 💡 BASE: 2 SYMBOLS: 0, 1 1 BYTE = 8 BITS 1 BIT can
2 BITS can store one of these 4 options: 00/ 01/ 10/11 (like a probability or as in 2 to the pow
3 BITS can store three of 8 options (2 to the power of three)
Binary to decimal:
The number (1001)2 in binary can be explained as: 1*2(3) + 0*2(2) + 0*2(1) + 1*2(0) = 8+
Where the 1*2(3) is the most significant bit (MSB). The 1*2(0) is the least sig
Fractional conversion:
(0101.011)2 = two parts: a real part / fraction
Real part = 0101 = 0*2(3) + 1*2(2) + 0*2(1) + 1*2(0) = 4 + 1 = (5)10
Fraction = 0.011 = 0*2(-1) + 1*2(-2) + 1*2(-3) = 0.125 + 0.25 = 0.375
Binary to octal:
When converting to octal, always start with binary.
(100001)2 = divide into three-digit parts starting from right:
421 421
100 001
4 1
لو الرقم تحته واحد بجمع الي فوق
Then the number in octal will be (41)8
Binary to Hexadecimal:
(100001)2 in binary to hexadecimal is the number (21)16.
Divide to four-digit parts starting from right: (if there are no numbers enough add zeros)
8421 8421
0010 0001
2 1
Octal number system:
💡 BASE: 8 SYMBOLS: 0, 1, 2, 3, 4, 5, 6, 7.
