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J277 1.2.4 Binary foundations

Part 1 of 5 · J277 1.2.4 · Number systems

The starting point for binary in OCR J277 section 1.2, building place value before any conversion is attempted.

Students will:

  • explain why computers represent data using binary
  • use the place values in an 8-bit binary number
  • identify the most significant and least significant bit
  • distinguish the number of values from the maximum value
  • explain why leading zeros do not change a value

Inside: 6 explanation cells, 2 number grids, 3 multiple-choice questions, 1 fill-in-the-blanks cell and 2 written answers. 22 marks, about 60 minutes.

Series: J277 1.2.4 · Number systems, part 1 of 5.

Shared by Coding PathwayVerified teacher

  • 14 cells
  • About 60 minutes
  • CC BY-SA 4.0
  • Shared 17 Aug 2026
  • Updated 9 Sept 2026

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The whole resource, exactly as a class sees it. Answers and marking are held back.

Number systems 1: binary foundations

Binary can look unfamiliar because it uses only two digits. The method becomes much easier once each column has a clear place value. Take one idea at a time and use the checks as evidence of what you can already do.

By the end of this worksheet, you should be able to:

  • explain why computers represent data using binary
  • use the place values in an 8-bit binary number
  • identify the most significant bit and least significant bit
  • distinguish the number of values from the maximum value
  • explain why leading zeros do not change a number's value

Work through the explanation, checks and applications in order. Use the final challenge to explain the method as well as use it.

1. Why binary?

Digital electronic circuits can reliably represent two distinct states, often described as on and off. We represent these states using the binary digits 1 and 0.

A bit is one binary digit. Four bits make a nibble, and eight bits make a byte. Text, images, sound and program instructions must all be represented in binary before a computer can process them.

Binary is a base 2 number system because it uses two possible digits. Denary is base 10 because it uses the ten digits 0 to 9.

The diagram shows the representation link. Binary digits are labels for the two reliably distinguishable circuit states; they are not tiny physical numbers moving through a wire.

Two electronic states represented by binary digits An off or low electronic state is represented as binary zero, while an on or high electronic state is represented as binary one. Reliable hardware state → binary representation OFF / LOW one reliable electronic state 0 ON / HIGH the other reliable electronic state 1 Two states can encode one bit; sequences of bits represent data and instructions.
Multiple choice1 mark

Why do digital computer systems represent data using binary?

  • ABinary automatically reduces every file to half its size
  • BElectronic circuits can represent two states, which can be recorded as 0 and 1
  • CBinary allows a processor to store an unlimited number
  • DPeople find long binary numbers easier to read than denary numbers

2. Eight binary place values

In denary, each column is ten times the column to its right. In binary, each column is twice the column to its right.

For the 8-bit numbers used here, the place values are:

1286432168421

A 1 means that the place value is included. A 0 means that it is not included.

For example, 00101001 contains 1s in the 32, 8 and 1 columns, so its value is 32 + 8 + 1 = 41.

Fill in the blanks6 marks
A single binary digit is a label 1. Binary is a label 2 number system. Four bits make a label 3, while eight bits make a label 4. The leftmost bit is the label 5 and the rightmost bit is the label 6.
  • byte
  • base 10
  • least significant bit
  • nibble
  • most significant bit
  • bit
  • base 2
  • hexadecimal

3. Number of values and maximum value

With n bits, there are 2^n different bit patterns. One pattern represents zero, so the largest value in the range is one less:

  • number of different values: 2^n
  • smallest value: 0
  • maximum value: 2^n - 1

For 4 bits, there are 2^4 = 16 different values, from 0 to 15.

For 8 bits, there are 2^8 = 256 different values, from 0 to 255.

Do not swap how many values with the maximum value. Zero occupies one of the possible patterns, so the maximum is one less than the number of values.

Number systems4 marks

Find either the number of values or the maximum value for each bit width.

Use 2^n for the number of values. Subtract 1 only when the question asks for the maximum value.

a)How many different values can 5 bits represent?

AnswerNot answered

b)What is the largest denary number 6 bits can hold?

AnswerNot answered

c)What is the largest denary number 3 bits can hold?

AnswerNot answered

d)How many different values can 6 bits represent?

AnswerNot answered
Multiple choice1 mark

Which statement about the values represented by 4 bits is correct?

  • AIt represents 15 values, from 1 to 15
  • BIt represents 16 values, from 1 to 16
  • CIt represents 15 values, from 0 to 14
  • DIt represents 16 values, from 0 to 15

4. Width, MSB and LSB

The most significant bit (MSB) is the leftmost bit. In the 8-bit numbers used here, its place value is 128.

The least significant bit (LSB) is the rightmost bit. Its place value is 1.

Leading zeros do not change a number's value. For example:

11010 = 00011010

Both contain 1s in the 16, 8 and 2 columns, so both represent 26. However, if an exam question asks for an 8-bit answer, all eight positions must be written.

Number systems3 marks

Use the place-value headings to find the denary value of each 8-bit binary number.

Add only the place values above columns containing a 1.

a)What is 10100110 in denary?

Binary
10100110
DenaryNot answered

b)What is 11111100 in denary?

Binary
11111100
DenaryNot answered

c)What is 11111010 in denary?

Binary
11111010
DenaryNot answered
Written answer2 marks

Explain why 11010 and 00011010 represent the same denary value, but why 00011010 may still be the required answer in an exam.

Refer to place values, leading zeros and an instruction asking for an 8-bit answer.

Students type their answer here.

Multiple choice, several answers2 marks

Which two statements are correct? Select two.

  • AThe LSB is the leftmost bit and has place value 128
  • BThe MSB is the leftmost bit and has place value 128
  • CAdding leading zeros always doubles the represented value
  • DThe LSB is the rightmost bit and has place value 1
Written answer3 marks

Challenge: without listing every pattern, determine how many different values 7 bits can represent and the maximum denary value. Explain why the two answers differ by one.

Apply 2^n, then account for zero.

Students type their answer here.

Independent check

Without looking back, complete these sentences aloud or on paper:

  1. Computers use binary because...
  2. The eight place values are...
  3. The MSB is...
  4. The LSB is...
  5. With n bits, the number of values is...
  6. With n bits, the maximum value in the range is...
  7. Leading zeros...

If one answer feels uncertain, return to that section and complete one more example. Secure foundations make every later conversion easier.