例題 1 Example 1：二進制轉十進制 Binary to decimal
把 1101101₂ 轉為十進制。Convert 1101101₂ to a decimal number.
1×64 + 1×32 + 0×16 + 1×8 + 1×4 + 0×2 + 1×164 + 32 + 8 + 4 + 1
答案： Answer: 109
【二進制及十六進制：數系轉換】Binary and Hexadecimal: Converting Between Number Bases
SketchMath 數學團隊 SketchMath Maths Team ｜ 更新 Updated 2026-10-20
二進制只用數字 0 及 1，位值是 1, 2, 4, 8, …。十六進制用 0–9 及 A–F（A = 10 … F = 15），位值是 1, 16, 256, …。二進制由右至左每四位一組，便可轉為十六進制。Binary uses the digits 0 and 1 with place values 1, 2, 4, 8, …. Hexadecimal uses 0–9 and A–F (A = 10 … F = 15) with place values 1, 16, 256, …. Group binary digits in fours from the right to change to hexadecimal.
數系重點 Number Base Facts
二進制轉十進制Binary to decimal把數字為 1 的位值相加Add the place values where the digit is 1
十進制轉二進制Decimal to binary不斷除以 2，餘數由下而上讀出Divide by 2 repeatedly; read the remainders upwards
十六進制數字Hexadecimal digits
A = 10, B = 11, C = 12, D = 13, E = 14, F = 15二進制轉十六進制Binary to hexadecimal由右至左每 4 位一組Group in 4 bits from the right
二進制及十六進制例題詳解 Worked Examples
例題 2 Example 2：十進制轉二進制 Decimal to binary
把 109 轉為二進制。Convert 109 to binary.
- 不斷除以 2：109、54、27、13、6、3、1，餘數依次是 1、0、1、1、0、1、1Divide by 2: 109, 54, 27, 13, 6, 3, 1 with remainders 1, 0, 1, 1, 0, 1, 1
- 由下而上讀出餘數：
1101101Read the remainders from the bottom:1101101
答案： Answer: 1101101₂
例題 3 Example 3：二進制轉十六進制 Binary to hexadecimal
把 10111100₂ 轉為十六進制。Convert 10111100₂ to hexadecimal.
- 每四位一組：
1011 | 1100Group in fours:1011 | 1100 1011 = 11 = B,1100 = 12 = C
答案： Answer: BC₁₆
💡 應試陷阱與秘訣 Exam Traps & Secrets
⚠️ 餘數要由下而上讀 Read the remainders upwards第一個餘數是最後一位數字，由上而下讀會把數字倒轉。The first remainder is the last digit. Reading from the top reverses the number.
✏️ 自我測試：互動練習 Self-Test: Interactive Practice
溫習方法：點擊以下任何題目，即時在坐標網格載入並核對計算步驟。How to study: click any question to load it on the coordinate grid and check your steps.
(十六進制轉十進制 Hex to decimal)把 3A₁₆ 轉為十進制。Convert 3A₁₆ to decimal.
(十進制轉十六進制 Decimal to hex)把 255 轉為十六進制。Convert 255 to hexadecimal.
(二進制加法 Binary addition)以二進制計算 1011₂ + 110₂。Add 1011₂ and 110₂ in binary.
常見問題 Frequently Asked Questions
電子電路有「開」與「關」兩種明確狀態，剛好對應數字 0 及 1。
Electronic circuits have two clear states, on and off, which match the two digits 0 and 1.
它屬中學數系的內容，常見於學校測驗。請向校內進度表核實你的年級是否須要。
It is taught in the secondary number-system work and appears in many school tests. Check your school scheme of work for what applies to your year.
把每個十六進制數字寫成 4 位二進制數，例如 B = 1011、C = 1100。
Write each hexadecimal digit as 4 binary digits, for example B = 1011 and C = 1100.