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STIG AS Level: BCD

Last updated 6 months ago
10 questions
What is BCD?
1
Draggable itemCorresponding Item
1011
Hexadecimal
1000 1000
Binary
-21
2's Complement
7A
Binary Coded Decimal
1
Draggable itemCorresponding Item
-21 (2s complement)
79
121 in hexadecimal
240
11110000 into denary (decimal)
11101011
81 (BCD)
1000 0001
1

Explain how 901 is 100100000001 in BCD

Binary Coded Decimal (BCD) is a way to represent decimal numbers (the numbers we commonly use, which are base-10) in a binary format (base-2). In BCD, each digit of a decimal number is represented by its own binary sequence.

How BCD Works:

  • Each digit in the decimal number is separately converted to a 4-bit binary equivalent.
  • For example, the decimal digit "5" is represented by the binary number "0101" in BCD.
  • The decimal digit "9" is represented by "1001" in BCD.

Example:

Let's take the decimal number 593.
  1. First, break it down into its individual digits: 5, 9, and 3.
  2. Convert each digit into a 4-bit binary number:
5 in binary is 0101. 9 in binary is 1001. 3 in binary is 0011.
so 593 is = 0101 1001 0011 (BCD)
3

Describe how an 8-bit BCD representation can be converted into a denary integer.
Give an example in your answer.

1

Describe how denary integers larger than 9 can be converted into BCD.
Give an example in your answer.

1

Match Up

1

Convert the following denary integer into Binary Coded Decimal (BCD). 653

1

State how you can recognise that this is not a valid BCD representation

Where is BCD used?

1. Digital Clocks and Watches

  • Display: BCD is used to drive the display of digits in digital clocks and watches. Each digit of the time is stored and manipulated as a separate BCD number, making it easy to convert directly to the 7-segment display format.

2. Calculators

  • Arithmetic Operations: Calculators often use BCD to perform arithmetic operations on decimal numbers. This is because BCD allows easier handling of decimal digits, avoiding errors that could arise from floating-point binary arithmetic.

3. Digital Displays (e.g., 7-Segment Displays)

  • Representation: In devices that use 7-segment displays (like fuel pumps, elevator floor indicators, or basic digital meters), BCD is commonly used to represent each digit of a number directly, making it simpler to drive the segments of the display.

4. Financial Applications

  • Exact Decimal Representation: In financial systems, BCD is sometimes used to ensure that decimal numbers (like currency) are represented exactly, without the rounding errors that can occur in binary floating-point representations.
1

Research your own BCD application and explain here

1

Describe a practical application where BCD is used.