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1CP2-P-1.2 Unsigned 8-bit binary and denary

Part 2 of 5 · 1CP2-P-1 · Binary foundations

The second Principles worksheet, attaching place values to the eight bits so students can convert accurately in both directions.

Students will:

  • use the correct terminology for width, most significant bit and least significant bit
  • convert 8-bit binary to denary using place values
  • convert denary to 8-bit binary, padding to the full width
  • explain why the width is part of the answer, not decoration
  • check a conversion before accepting it

Inside: 9 explanation cells, 1 multiple-choice question, 4 number cells, 2 fill-in-the-blanks cells and 1 written answer. 20 marks, about 45 minutes.

Series: 1CP2-P-1 · Binary foundations, part 2 of 5.

Shared by Coding PathwayVerified teacher

  • 17 cells
  • About 45 minutes
  • CC BY-SA 4.0
  • Shared 17 Aug 2026

Preview

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

Unsigned 8-bit binary and denary

You already know that 8 bits give 256 patterns and unsigned values from 0 to 255. This worksheet attaches place values to those bits so you can convert accurately in both directions.

1. Width and terminology

A nibble contains 4 bits. A byte contains 8 bits, or two nibbles. An unsigned integer represents zero or a positive whole number; no bit is reserved for a negative sign.

An answer requested as 8-bit binary must contain exactly eight bits. Leading zeroes preserve the stated width.

Fill in the blanks4 marks
A group of 4 bits is a label 1. A group of 8 bits is a label 2. A whole-number representation with no negative values is label 3. Its 8-bit range ends at label 4.
  • 127
  • 255
  • byte
  • nibble
  • signed
  • unsigned

2. Binary to denary

Unsigned 8-bit place values00101101 = 32 + 8 + 4 + 1 = 45128643216842100101101A 1 selects its place value. A 0 does not contribute to the sum.

The headings double as you move left: 1, 2, 4, 8, 16, 32, 64, 128. Read them in the displayed left-to-right order as 128 64 32 16 8 4 2 1.

A bit set to 1 selects its heading. Add only those selected values.

Number systems3 marks

Convert each unsigned 8-bit pattern to denary.

Add the headings above every 1 bit. Show a place-value row to support the calculation.

a)What is 00101101 in denary?

Binary
00101101
DenaryNot answered

b)What is 10010010 in denary?

Binary
10010010
DenaryNot answered

c)What is 11100001 in denary?

Binary
11100001
DenaryNot answered

Make the working visible

For 01010110, select 64 + 16 + 4 + 2 and obtain 86.

A strong written method names the selected place values. It does not treat the pattern as the denary digits ten million one hundred and one thousand and ten.

Written answer2 marks

Show how the unsigned pattern 10100110 converts to denary.

List the selected place values and give their total.

Students type their answer here.

3. Denary to 8-bit binary

Use the largest-fitting-place method for denary 104:

  1. 128 does not fit, so write 0.
  2. 64 fits; write 1 and calculate 104 − 64 = 40.
  3. 32 fits; write 1 and calculate 40 − 32 = 8.
  4. 16 does not fit; write 0.
  5. 8 fits; write 1 and the remainder becomes 0.
  6. Write 0 under 4, 2 and 1.

Result: 01101000.

Check by adding 64 + 32 + 8 = 104.

Number systems3 marks

Convert each denary value to unsigned 8-bit binary.

Work from 128 to 1. Keep all eight positions and check by adding selected place values.

a)Convert 37 to 8-bit binary.

Binary

b)Convert 104 to 8-bit binary.

Binary

c)Convert 213 to 8-bit binary.

Binary

4. Width is part of the answer

Denary 13 can be written as 1101 when no width is specified. If the demand says 8-bit, the answer is 00001101.

The leading zeroes do not change the value. They show that the representation occupies the required eight positions. Pearson mark schemes can withhold conversion marks when an answer is not 8-bit.

Multiple choice1 mark

Which is the correct 8-bit unsigned representation of denary 19?

  • A10011
  • B00010011
  • C11101100
  • D00011001

5. Independent mixed conversion

Choose the method from the direction of the question:

  • binary to denary: add headings selected by 1 bits;
  • denary to binary: choose largest fitting headings and subtract;
  • in both directions: check the range and all eight positions.
Number systems2 marks

Convert these unsigned 8-bit patterns to denary.

Work without displayed place-value headings. Include the boundary pattern with every bit set.

a)What is 00000001 in denary?

Binary
00000001
DenaryNot answered

b)What is 11111111 in denary?

Binary
11111111
DenaryNot answered
Number systems3 marks

Convert these denary values to unsigned 8-bit binary.

Work without displayed place-value headings and give exactly eight bits for every answer.

a)Convert 64 to 8-bit binary.

Binary

b)Convert 129 to 8-bit binary.

Binary

c)Convert 255 to 8-bit binary.

Binary

6. Check before accepting an answer

Use three checks:

  1. Width: exactly eight bits where required.
  2. Range: unsigned 8-bit answers represent 0 to 255.
  3. Reverse check: add selected place values or reconstruct the pattern.

A pattern beginning with 1 is not automatically negative. It is negative only when the stated interpretation is signed two's complement, which is taught later.

Fill in the blanks2 marks
An unsigned 8-bit answer must contain label 1 bits and represent a value no greater than label 2.
  • 4
  • 8
  • 127
  • 255
  • 256

Ready for arithmetic

You can now convert unsigned 8-bit values in both directions and check width, range and leading zeroes.

Next, those same eight columns become an addition layout. Carries will be method steps; overflow will depend on whether the final value still fits into eight bits.