AS · Practice questions · Binary, denary, hexadecimal and BCD

Four ways to write it.

Six original Cambridge-style questions on number bases and BCD, with worked solutions.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

Nibbles are the key.

Binary and hex: one hex digit = one nibble; group from the right.
Hex to denary: place values 4096, 256, 16, 1.
BCD: one nibble per denary digit; 1010 to 1111 are invalid.
Uses: BCD for displays and money; hex for memory addresses, dumps, colours and MAC addresses.

Convert

[2 marks]

Convert the binary number 10011110 to (a) denary and (b) hexadecimal.

(a) 128 + 16 + 8 + 4 + 2 = 158. ✓
(b) 1001 = 9 and 1110 = E, so 9E. ✓

Convert

[2 marks]

Convert the denary number 300 to (a) 12-bit binary and (b) hexadecimal.

(a) 300 = 256 + 32 + 8 + 4, so 0001 0010 1100. ✓
(b) 0001 = 1, 0010 = 2, 1100 = C, so 12C. ✓

Convert

[2 marks]

Write the denary number 4709 in Binary Coded Decimal.

4 = 0100, 7 = 0111, 0 = 0000, 9 = 1001. ✓
0100 0111 0000 1001. ✓

Convert

[3 marks]

The 12 bits 1000 0110 0101 are stored in BCD. (a) Give the denary value. (b) Give the same value in hexadecimal.

(a) 1000 = 8, 0110 = 6, 0101 = 5, so 865. ✓
865 in binary is 0011 0110 0001 (512 + 256 + 64 + 32 + 1). ✓
(b) 361 in hexadecimal. ✓

Explain

[4 marks]

Describe one practical application of BCD and one practical application of hexadecimal. Justify each.

BCD: digital clock, calculator or meter display. ✓
Each digit is held in its own nibble and can be sent directly to its own display digit (or: money values are stored exactly with no rounding errors). ✓
Hex: memory addresses / memory dumps / MAC addresses / colour codes. ✓
Shorter and easier for people to read and check than binary, and it converts to binary easily (4 bits per digit). ✓

Analysis

[3 marks]

A register holds the byte 0100 1001. Explain why its value cannot be stated without knowing how it is represented, giving its value as an unsigned binary integer and as BCD.

A bit pattern only has meaning under a chosen representation. ✓
As an unsigned binary integer: 64 + 8 + 1 = 73. ✓
As BCD: 0100 = 4 and 1001 = 9, so 49. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.