CS101- Binary System
Zhenyu Yang
• Visiting Assistant Professor of Physics and Computer Science
• Research Assistant Professor of Medical Physics
• Assistant Director of Jiangsu Provincial University Key
(Construction) Laboratory for Smart Diagnosis and Treatment
of Lung Cancer
Fall 2025
Recap: computer science
• What is computer science?
• What is algorithm and computer programming?
Guess Game
• Randomly select a number between 1-30, DO NOT tell me
Card 1 Card 2 Card 3 Card 4 Card 5
Representing Data
• You must have seen computers do amazing things with
numbers, sounds, text, pictures, and games
❖ All these data from a computer’s eye are just “0” and “1”
Representing Data
• All the wonderful multi-media information on computers can
be represented by ON/OFF “switches” (transistor) in
computers.
binary digit 1
binary digit 0
Representing Data
• Computers are super electronic machines, use electricity for
data processing and storage, which is fast and reliable.
• Electricity can ow through switches:
❖ if the switch is on, the electricity ows; binary digit 1
❖ if the switch is o , the electricity does not ow binary digit 0
transistors transistors
fl
ff
fl
fl
Representing Data
• Computers represent data use binary system
• Binary is a mathematical number system: a way of counting.
❖ With millions of switches, we can represent a lot of information
binary digit 0
binary digit 1
Introduction to Number Base
• Normal decimal counting: 0~9 (base ten)
❖ Place value, from right to left raise by 10, 10 is the base
Introduction to Number Base
• Binary system has only two numbers: 0 and 1 (base 2)
❖ Place value, from right to left raise by 2, 2 is the base
Introduction to Number Base
• Binary system has only two numbers: 0 and 1 (base 2)
❖ Place value, from right to left raise by 2, 2 is the base
Binary to Decimal Number
• Positional Weight Summation
❖ directly summing the place value with the digit
Di erent Counting System
• A formal way to present number in di erent counting system
ff
ff
Binary to Decimal Number
• Q1: What is the decimal number for binary number 1011001？
Binary to Decimal Number
• Q1: What is the decimal number for binary number 1011001？
• Q2: Is there a faster way?
Binary to Decimal Number
• Current Decimal Value = Previous Decimal Value * 2 +
Current Binary Digit
❖ Doubling Adds Positional Weight: doubling the current decimal
value shifts its contribution one place to the left in binary,
equivalent to multiplying by 2 (e.g., 101 to 1010 when
multiplied by 2).
❖ Adding the Current Bit: adding the current binary digit
accounts for the new contribution at the least signi cant
position.
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Binary to Decimal Number
• Doubling Method
❖ Start with an initial value of 0.
❖ Traverse each binary digit from
left to right.
❖ For each digit
‣ double the current value
‣ add current binary digit (0 or 1)
Decimal to Binary Number
• Calculate binary number from decimal number
❖ Divide the number by 2 and record the remainder.
❖ Repeat until the quotient becomes 0.
❖ Read the remainders from bottom to top to form the binary
number.
Decimal to Binary Number
• What is the binary number for decimal number of 156?
Decimal to Binary Number
• What is the binary number for decimal number of 156?
Decimal to Binary Number
• What is the binary number for decimal number of 156?
Decimal to Binary Number
• Why it works?
1310 = 8+4+0+1 = 1*23+1*22+0*21+1*20 = 11012
=6
1310/2 = 6 reminder 1 1*22+1*21+0*20 + 1
610/2 = 3 reminder 0 1*21+1*20 + 0
310/2 = 1 reminder 1 1*20 + 1
110/2 = 0 reminder 1 1
Addition in Binary Number
Example 1 Example 2 Example 3
Addition in Binary Number
• Q3: What is the results of 11011 + 1011 in binary?
Addition in Binary Number
• Q3: What is the results of 11011 + 1011 in binary?
Answer = 1001102 = 3810
Subtraction in Binary Number
Subtraction in Binary Number
• Q3: What is the results of 101000 – 10001 in binary?
Answer = 101112 = 2310
Back to Guess Game
• Randomly select a number between 1-30, DO NOT tell me
Summary
• Binary Numbers Operation
❖ Decimal to binary
❖ Binary to decimal
❖ Binary Addition
❖ Binary subtraction
Bit and Byte
• What is bit (binary digit)?
❖ The smallest/basic unit of information in computer.
❖ have a value of either 0 or 1, and is the fundamental building
block of all digital computing and communication systems
Bit and Byte
• What is Byte?
❖ 1 Byte (1B) = 8 Bits (8b)
‣ With one bit (transistors) we can represent 0~1, with 8 bits
we can represent 0~255
‣ kilobyte (KB = 1000 bytes), megabytes (MB = 1000 KB),
gigabyte (GB = 1000 MB), terabyte (TB = 1000 GB)
❖ The most common units for document size DO NOT use 1024!
‣ Movie (~GB); Word/Pdf (~MB); Text (~KB)
Bit and Byte
Bit Rate (Info Transmission)
• Bit rate: number of bits transmitted per second
❖ Mbps: Mega bits per second
❖ Others: Kbps and Gbps
• Examples:
❖ Ethernet speed (wired transmission)
‣ Gigabit Ethernet (GbE), 2.5 Gigabit Ethernet (2.5GbE), 10
Gigabit Ethernet (10GbE)
❖ WiFi speed (wireless transmission)
‣ WiFi 5 (3.5 Gbps), WiFi 6 (9.6 Gbps), WiFi 7 (46 Gbps)
❖ 4G/5G speed (wireless transmission)
‣ 5G (10 Gbps), 4G (1 Gbps)
Bit Rate (Info Transmission)
• Bit rate: number of bits transmitted per second
❖ Mbps: Mega bits per second
❖ Others: Kbps and Gbps
• Examples:
❖ Ethernet speed (wired transmission)
‣ Gigabit Ethernet (GbE), 2.5 Gigabit Ethernet (2.5GbE), 10
Gigabit Ethernet (10GbE)
❖ WiFi speed (wireless transmission)
‣ WiFi 5 (3.5 Gbps), WiFi 6 (9.6 Gbps), WiFi 7 (46 Gbps)
❖ 4G/5G speed (wireless transmission)
‣ 5G (10 Gbps), 4G (1 Gbps)
❖ Test your own speed: https://www.speedtest.net
Bit Rate (Info Transmission)
• Bit rate: number of bits transmitted per second
❖ Mbps: Mega bits per second
❖ Others: Kbps and Gbps
• Examples:
Bit Rate (Info Transmission)
• Q1: if you have a 4K HD graduation video 1TB in your laptop
in Duke, how long does it take to transmit the le to DKU? (If
the average transmission speed between Duke and DKU is
8Mbps)
❖ Be careful about “B” & “b”
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Bit Rate (Info Transmission)
• Q1: if you have a 4K HD graduation video 1TB in your laptop
in Duke, how long does it take to transmit the le to DKU? (If
the average transmission speed between Duke and DKU is
8Mbps)
❖ Be careful about “B” & “b”
‣ Time = Size / Speed
‣ Size = 1TB = 1000 * 1000 MB = 1000 * 1000 * 8 Mb
‣ Time = 1000 * 1000 s =11.57 days
fi
