chapter 1

What is the binary system?

• Base 2 number system.

• Values: 0 (OFF) and 1 (ON).

• MSB: Most Significant Bit (leftmost bit).

What is the denary system?

• Base 10 number system.

• Values: 0 to 9

What is the hexadecimal system?

• Base 16 number system.

• Values: 0-9 and A-F (A=10, B=11, ..., F=15).

How do you convert hexadecimal to binary?

1. Separate each hex digit.

2. Convert each hex digit to 4-bit binary.

3. Combine binary values.

How do you convert binary to hexadecimal?

1. Group binary digits into 4-bit sections (from right).

2. Add leading 0s if needed.

3. Convert each group to hexadecimal.

How do you convert hexadecimal to denary?

1. Convert hex to binary.

2. Convert binary to denary.

How do you convert denary to hexadecimal?

1. Convert denary to binary.

2. Convert binary to hexadecimal.

What is overflow in binary calculations?

• Occurs when the result exceeds the bit limit.

• E.g., adding two 8-bit values results in a 9-bit answer.

What is a logical shift?

• Moves binary digits left or right.

• Emptied bits replaced with 0.

How do you perform a left logical shift?

• Remove leftmost bit.

• Shift all bits left.

• Add 0 to the rightmost position.

What is two's complement?

• Method to represent negative binary values.

• MSB indicates the sign (-128 for 8 bits).

How do you convert a binary number to its two's complement?

1. Find the first 1 from the right.

2. Flip all bits to the left of it.

How do you convert a two's complement binary to denary?

1. Replace MSB with its negative value.

2. Add the remaining values.

Where is hexadecimal used?

• HTML colors.

• MAC addresses.

• Assembly language.

• Memory dumps.

• Debugging.

• Error codes.

• IP addresses.

What is ASCII?

• 7-bit code for characters and control codes.

• Uppercase and lowercase have different values.

• "a" = 97, "b" = 98, etc.

How is Unicode different from ASCII?

• Unicode supports more characters (up to 4 bytes).

• Includes international languages.

• First 128 values match ASCII.