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Questions and Answers
What is the product of multiplying two single-bit numbers 1 and 1 in a binary system?
What is the first step in converting a decimal number to any radix number?
What method is used to convert the fractional part of a decimal number to any radix number?
What is the result of multiplying two single-bit numbers 0 and 1 in a binary system?
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What is the purpose of the successive division method in radix conversion?
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How many steps are involved in converting a decimal number to any radix number?
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What is the result of multiplying two single-bit numbers 1 and 0 in a binary system?
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What is the method used to convert the integer part of a decimal number to any radix number?
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What is the purpose of the successive multiplication method in radix conversion?
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What is the result of multiplying two single-bit numbers 0 and 0 in a binary system?
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Study Notes
Introduction to Number Systems
- Digital logic systems can perform numerical computations using a binary number system.
- Humans use the decimal system, but digital machines use binary due to the availability of two-state devices (transistors).
- Other number systems used in conjunction with programmable logic devices include hexadecimal.
Characteristics of Numbering Systems
- Digits are consecutive.
- The number of digits equals the base size.
- Zero is always the first digit.
- The base number is never a digit.
- When 1 is added to the largest digit, a sum of zero and a carry of one results.
Significant Digits
- Most significant digit (MSD) and least significant digit (LSD) are important concepts in number systems.
Binary Number System
- Also known as the Base 2 system.
- Used to model electrical signals in computers.
- 0 represents no voltage or an off state, and 1 represents presence of voltage or an on state.
Binary Numbering Scale
- Each positional value is a power of 2.
Binary Addition
- There are 4 possible binary addition combinations.
Decimal to Binary Conversion
- The easiest way to convert a decimal number to binary is using the Division Algorithm.
- This method repeatedly divides a decimal number by 2 and records the quotient and remainder.
Binary to Decimal Conversion
- The easiest method for converting a binary number to decimal is using the Multiplication Algorithm.
- Multiply the binary digits by increasing powers of 2, starting from the right, and sum the products.
Octal Number System
- Also known as the Base 8 System.
- Uses digits 0-7.
- Readily converts to binary.
- Groups of three binary digits represent each octal digit.
Decimal to Octal Conversion
- Convert a decimal number to octal by repetitively dividing by 8 and recording the remainder.
Octal to Decimal Conversion
- Convert an octal number to decimal by multiplying each digit by its positional value and summing the products.
Octal to Binary Conversion
- Each octal digit converts to 3 binary digits.
Hexadecimal Number System
- Base 16 system.
- Uses digits 0-9 and letters A-F.
- Each hexadecimal digit represents 4 binary digits.
Decimal to Hexadecimal Conversion
- Convert a decimal number to hexadecimal by repetitively dividing by 16 and recording the remainder.
Hexadecimal to Decimal Conversion
- Convert a hexadecimal number to decimal by multiplying each digit by its positional value and summing the products.
Binary to Hexadecimal Conversion
- Use a substitution code to convert binary to hexadecimal.
Complementary Arithmetic
- 1's complement: switch all 0's to 1's and 1's to 0's.
- 2's complement: find the 1's complement and add 1.
Signed Numbers
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Need to represent both positive and negative numbers.
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Three representations: signed magnitude, signed 1's complement, and signed 2's complement.### Binary Operations
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Rules for adding two single-bit numbers:
- A=0, B=0: Sum=0, Carry=0
- A=0, B=1: Sum=1, Carry=0
- A=1, B=0: Sum=1, Carry=0
- A=1, B=1: Sum=0, Carry=1
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Rules for subtracting two single-bit numbers:
- A=0, B=0: Difference=0, Borrow=0
- A=0, B=1: Difference=1, Borrow=1
- A=1, B=0: Difference=1, Borrow=0
- A=1, B=1: Difference=0, Borrow=1
Binary Multiplication
- Rules for multiplying two single-bit numbers:
- A=0, B=0: Product=0
- A=0, B=1: Product=0
- A=1, B=0: Product=0
- A=1, B=1: Product=1
Conversion of Decimal Numbers to Any Radix Number
- Conversion of decimal numbers to any radix number involves two steps:
- Step 1: Convert the integer part using successive division method
- Step 2: Convert the fraction part using successive multiplication method
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Quiz about Seiyun University's College of Applied Science, CS department, covering information technology and faculty details.
