Laws of integral indices · Ages 13–14
Hexadecimal numbers
A to F are 10 to 15; place values 1, 16, 256.
How to do it
Method
A to F are 10 to 15; place values 1, 16, 256
2F₁₆ = 2 × 16 + 15 = 47
Another way
Binary in groups of four
11001000₂: 1100 = 12 = C and 1000 = 8, so C8₁₆
In full
Hexadecimal uses sixteen digits: 0 to 9, then A, B, C, D, E and F for 10, 11, 12, 13, 14 and 15. Its place values are powers of 16: from the right, 1, 16, 256, 4096, …. Hexadecimal to decimal: expand it, 2F₁₆ = 2 × 16 + 15 = 47, and 1A3₁₆ = 1 × 256 + 10 × 16 + 3 = 419. Decimal to hexadecimal: divide by 16 again and again. 200 ÷ 16 = 12 r 8, 12 ÷ 16 = 0 r 12; read from the bottom up, writing 12 as C, so 200 = C8₁₆. Hexadecimal and binary convert straight into each other, since 16 = 24: each hexadecimal digit is exactly four binary digits. Group the binary digits in fours from the right: 11001000₂ splits into 1100 and 1000, which are 12 and 8, so it is C8₁₆.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
As a decimal number: A40₁₆ =
Show the answer and working
Answer: 2624
From the right the place values are 1, 16, 256: 10 × 256 + 4 × 16 + 0 = 2624.
Example 2
What is 1100100₂ in hexadecimal?
- A. 46₁₆
- B. 64₁₆
- C. 100₁₆
- D. C4₁₆
Choose the right answer
Show the answer and working
Answer: B. 64₁₆
Group in fours from the right: the left group is 6, the right 4, so 64₁₆.
Example 3
As a decimal number: 86₁₆ − 27₁₆ =
Show the answer and working
Answer: 95
As decimals first: 134 − 39 = 95.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.DB₁₆ = × 16 + =
Fill in each blank
Answer:
2.As a decimal number: 27₁₆ =
Answer:
3.In binary: in CA₁₆, C = ₂ and A = ₂, so CA₁₆ = ₂
Fill in each blank
Answer:
4.What is 1001111₂ in hexadecimal?
- A. 4F₁₆
- B. 97₁₆
- C. F4₁₆
- D. 79₁₆
Choose the right answer
Answer:
5.25₁₆ is bigger than 29.
True or false?
Answer:
All the answers
- 1. 13, 11, 219
- 2. 39
- 3. 1100, 1010, 11001010
- 4. A. 4F₁₆
- 5. True
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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