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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 and understanding binary range.

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 text sections, 1 multiple-choice activity, 3 completion activities, 3 written answers, 2 number activities. 18 marks. Suggested teaching time: 40–55 minutes. 1 diagram.

Includes a teacher guide with suggested sections, timings and common misconceptions.

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

Shared by Coding PathwayVerified teacher

  • 15 cells
  • About 45 minutes
  • CC BY-SA 4.0
  • Shared 17 Aug 2026
  • Updated 27 Oct 2026

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

Binary foundations

Binary uses two digits: 0 and 1. You will use these digits to represent values, then distinguish the number of possible values from the largest value.

1. Why binary?

Digital circuits contain transistors, which can act as switches. Their two distinguishable states can be represented by 0 and 1.

A bit is one binary digit. Four bits make a nibble; eight bits make a byte. Binary is base 2, while denary is base 10. Text, images, sound and instructions are all represented in binary for processing.

Two circuit states represented by binary digits Digital hardware can distinguish two states. In this example a low state represents zero and a high state represents one. The digits represent states; they are not physical numbers in the wire. Two distinguishable states Low state High state 0 1 A bit records one of the two states.
Multiple choice1 mark

Why is binary suitable for digital electronic circuits?

  • AIt always makes files smaller
  • BIt represents the two distinguishable states of switches
  • CIt can represent unlimited values in one byte
  • DIt removes the need for hardware
Fill in the blanks4 marks
A binary digit is a Answer 1. Binary is Answer 2. Four bits make a Answer 3, and eight bits make a Answer 4.
  • bit
  • base 10
  • nibble
  • base 2
  • byte

2. Positions matter

Each binary column is twice the value of the column to its right.

1286432168421

A 1 includes that column's value. A 0 does not. For example, 00101001 represents 32 + 8 + 1 = 41.

The leftmost bit is the most significant bit (MSB). The rightmost is the least significant bit (LSB). In an eight-bit number, their place values are 128 and 1.

Fill in the blanks2 marks
In an eight-bit number, the leftmost bit is the Answer 1 and the rightmost bit is the Answer 2.
Number systems2 marks

Find the denary values. Use the place-value headings.

a)What is 00010010 in denary?

Binary
00010010
DenaryNot answered

b)What is 01000001 in denary?

Binary
01000001
DenaryNot answered
Fill in the blanks1 mark
The eight-bit value 00000000 represents denary Answer 1.

3. Count or maximum?

With n bits there are 2^n different patterns. One represents zero, so the maximum value is 2^n − 1.

Four bits give 16 values, from 0 to 15. Eight bits give 256 values, from 0 to 255. 256 values does not mean a maximum value of 256.

Number systems4 marks

Find the requested count or maximum. Read each question carefully.

a)How many different values can 4 bits represent?

AnswerNot answered

b)What is the largest denary number 4 bits can hold?

AnswerNot answered

c)How many different values can 8 bits represent?

AnswerNot answered

d)What is the largest denary number 8 bits can hold?

AnswerNot answered
Written answer1 mark

Eight bits represent 256 values, but the largest is 255. Explain the difference.

Students type their answer here.

4. Leading zeros

11010 and 00011010 both represent 16 + 8 + 2 = 26. Adding zeros at the left adds no value. If a question asks for eight bits, include all eight positions.

Written answer2 marks

Explain why 11010 and 00011010 have the same value, but why the longer form may be required.

Students type their answer here.

Written answer1 mark

State a hardware reason why computers use binary to represent data.

Students type their answer here.

Review

Choose one answer to improve. Check whether the difficulty was the hardware explanation, a place value, the width or the difference between a count and a maximum.