Number Representations
What is Number Representations?
A binary digit, representing either 0 or 1.
Key formula / rule: Unsigned Number Range
Key points
- Understand the need for different number representations.
- Differentiate between unsigned and signed number representations.
- Explain the principles of signed magnitude, one's complement, and two's complement.
- Perform conversions between decimal and binary representations.
Common exam trap
Confusing the range of different representations for the same number of bits.
Definitions
- Term
Bit
- Meaning
A binary digit, representing either 0 or 1.
- Term
MSB
- Meaning
Most Significant Bit; the leftmost bit in a binary number, often used as a sign bit in signed representations.
- Term
Two's Complement
- Meaning
A system for representing signed integers where negative numbers are formed by inverting all bits of the positive number and adding 1.
- Term
BCD
- Meaning
Binary Coded Decimal; a system where each decimal digit is represented by a 4-bit binary code.
Learning objectives
Understand the need for different number representations.
Differentiate between unsigned and signed number representations.
Explain the principles of signed magnitude, one's complement, and two's complement.
Perform conversions between decimal and binary representations.
Understand the BCD representation.
Identify the advantages of two's complement representation.
Formulae
- Name
Unsigned Number Range
- Note
For an n-bit unsigned integer.
- Expression
0 to 2n - 1
- Name
Two's Complement Number Range
- Note
For an n-bit two's complement integer.
- Expression
-2^(n-1) to 2^(n-1) - 1
- Name
Two's Complement Conversion
- Note
Where NOT X is the bitwise inversion of X.
- Expression
Two's Complement of X = (NOT X) + 1
Prerequisites
Binary Number System
Decimal Number System
Basic Arithmetic Operations
Common mistakes
Confusing the range of different representations for the same number of bits.
Incorrectly calculating the two's complement of a number.
Assuming all systems use the same representation for negative numbers.
Applying arithmetic rules for one representation to another.
Overlooking the sign bit's role in determining the value.
Keywords
Number Representation
Binary
Unsigned
Signed Magnitude
One's Complement
Two's Complement
BCD
MSB
Bitwise Operations
Practice preview
Which number system uses a base of 16?…
easy
What is the BCD representation of the decimal number 87?…
medium
What is the IEEE 754 single-precision floating-point representation of the decimal number -0.75?…
hard