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OCR J277 · Component 1 · Topic 1.2.4a

Binary &
Denary
Conversion

Place Values · MSB & LSB · Binary → Denary · Denary → Binary

CSZone OCR GCSE Computer Science J277
Learning Objectives

By the end of this video you will be able to...

Identify and use the 8-bit place values: 128, 64, 32, 16, 8, 4, 2, 1
Explain the terms most significant bit (MSB) and least significant bit (LSB)
Convert any binary number (8 bits) to its denary equivalent
Convert any denary number (0–255) to its 8-bit binary equivalent
Write any binary number using leading zeros to fill all 8 bit positions
⚡ Binary↔Denary conversions appear in every OCR J277 paper — the place value method is the only reliable approach
The Binary Number System

Binary uses 8 place values — each column doubles

1286432168421
2⁷2⁶2⁵2⁴2³2²2¹2⁰
Each column is worth double the column to its right — just like denary columns are worth 10× each time
A 1 in a column means that value is included in the total — a 0 means it is not included
With 8 bits the maximum value is 128+64+32+16+8+4+2+1 = 255 and the minimum is 00000000 = 0
SPEC REQUIREMENT
The OCR spec requires denary range 0–255 and binary range 00000000–11111111 (8 bits)
Key Terms

Most Significant Bit & Least Significant Bit

128
MSB		 643216842 1
LSB
bit 7 bit 6bit 5bit 4bit 3bit 2bit 1 bit 0
MOST SIGNIFICANT BIT (MSB)
The leftmost bit — has the highest place value (128). It has the most influence on the total value. Also called bit 7.
LEAST SIGNIFICANT BIT (LSB)
The rightmost bit — has the lowest place value (1). It has the least influence on the total value. Also called bit 0.
The MSB and LSB are OCR spec vocabulary — you must know both terms and be able to identify them
Binary → Denary

Method: add together the place values where the bit is 1

STEP-BY-STEP METHOD
Step 1: Write out the 8 place values: 128, 64, 32, 16, 8, 4, 2, 1
Step 2: Place each binary digit under the correct column
Step 3: Add up all place values where the binary digit is 1
Step 4: The total is your denary answer
Example: Convert 00110001 to denary
1286432168421
0011 0001
——3216 ———1
32 + 16 + 1 = 49
00110001 in binary equals 49 in denary — confirmed in the OCR 2023 mark scheme
Binary → Denary

Worked example: 11110100

Convert 11110100 to denary — step by step
1286432168421
1111 0100
128643216 —4——
128 + 64 + 32 + 16 + 4 = 244
11110100 = 244 — this exact conversion appears in the OCR 2023 mark scheme (Q1b)
Quick check: the bits set are 128+64+32+16 = 240, plus 4 = 244. Always check your working by adding the values once more.
Denary → Binary

Method: work left to right through the place values

COLUMN METHOD — 4 STEPS
Step 1: Write out the place values: 128, 64, 32, 16, 8, 4, 2, 1
Step 2: Starting at 128 — if your number is ≥ that value, write a 1 and subtract it. Otherwise write 0.
Step 3: Move to the next column and repeat with the remainder
Step 4: Continue until all 8 columns are filled — you must always write 8 bits
Example: Convert denary 102 to 8-bit binary
Denary → Binary

Worked example: 102 → binary

102 < 128 → write 0, remainder still 102
102 ≥ 64  → write 1, remainder: 102 − 64 = 38
38  ≥ 32  → write 1, remainder: 38 − 32 = 6
6   < 16  → write 0, remainder still 6
6   < 8   → write 0, remainder still 6
6   ≥ 4   → write 1, remainder: 6 − 4 = 2
2   ≥ 2   → write 1, remainder: 2 − 2 = 0
0   < 1   → write 0
Result: 01100110 = 102 ✓
This exact conversion (102 → 01100110) appears in the OCR 2023 mark scheme — Q1b
8-Bit Rule

Answers must always be written as 8 bits

THE RULE
The OCR spec states: "Ability to deal with binary numbers containing between 1 and 8 bits (e.g. 11010 is the same as 00011010)"
✗ WRONG — loses the mark
11010
Only 5 bits — incomplete
✓ CORRECT — full marks
00011010
8 bits with leading zeros
The mark scheme states answers "must be 8-bits" — missing leading zeros loses the mark even if the value is correct
Small values like 7 in denary become 00000111 — you must include all five leading zeros
Exam Practice

Exam Question 1

Question 1 — style from OCR J277/01 June 2023 Q1b · 4 marks
Complete the table below. Convert each denary number to its 8-bit binary equivalent.
4 marks — 1 per row
Denary 8-bit binary
7 00000111
49 00110001
102 01100110
244 11110100
MS NOTE
Must be 8 bits. Answers with fewer bits score 0 even if the bits present are correct.
Exam Practice

Exam Question 2

Question 2 · 2 marks
Convert the 8-bit binary number 10101010 to denary. Show your working.
2 marks
1286432168421
1010 1010
128—32— 8—2—
128 + 32 + 8 + 2 = 170
M1
Correct working shown — place value table or equivalent
M2
Answer: 170
Exam Practice

Exam Question 3

Question 3 · 3 marks
a) Convert denary 200 to 8-bit binary.    b) State the value of the most significant bit in your answer.    c) State the value of the least significant bit in your answer.
3 marks
Part a — denary 200 → binary
1286432168421
1100 1000
128 + 64 + 8 = 200 ✓
11001000
PART b — MSB
The MSB is the leftmost bit.
In 11001000, the MSB = 1
PART c — LSB
The LSB is the rightmost bit.
In 11001000, the LSB = 0
Common Mistakes

Four mistakes that cost marks in the exam

1
Not writing 8 bits. The mark scheme says answers must be 8 bits. Writing 110001 instead of 00110001 scores zero even if the binary digits present are correct. Always pad with leading zeros to fill all 8 columns.
2
Wrong place values. The columns are 128, 64, 32, 16, 8, 4, 2, 1 — not 256, 128, 64... and not starting from 1 on the left. Memorise this sequence. The most common error is shifting all values one column left or right.
3
Confusing MSB and LSB. MSB = leftmost bit = highest place value (128). LSB = rightmost bit = lowest place value (1). Getting them swapped loses the mark on any question that names these terms.
4
Not showing working for denary → binary. The mark scheme awards separate marks for working and for the final answer. If you write only the binary answer with no working shown, you can lose the working mark even if the answer is correct.
Summary

1.2.4a — Binary & Denary Conversion

PLACE VALUES
128 · 64 · 32 · 16 · 8 · 4 · 2 · 1
Range: 0 (00000000) → 255 (11111111)
MSB & LSB
MSB = leftmost bit (128) · LSB = rightmost bit (1)
8-BIT RULE
Always write 8 bits — pad with leading zeros. 11010 must be written 00011010
BINARY → DENARY
Add up place values where bit = 1
00110001 = 32+16+1 = 49
DENARY → BINARY
Work left to right — if number ≥ column value, write 1 & subtract; else write 0
102 = 01100110
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That's 1.2.4a done.

Next up: 1.2.4b — Hexadecimal Conversion

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