Digital Signal Representation

Number Systems and Their Bases

• The decimal number system operates on a base of 10.
• The binary system consists of 2 digits: 0 and 1.
• The hexadecimal system has a base value of 16.

Digital Signal Terminology

• The time required to send one bit in a digital signal is known as 'bit time.'
• 'Bit rate' refers to the number of bits transmitted per unit of time, typically measured in bits per second (bps).

Number Representations

• In the decimal number system, there are 10 basic digits: 0 through 9.
• The hexadecimal system includes 16 digits, comprising 0-9 and letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15).

Binary and Octal Conversions

• The weight of the least significant bit (LSB) in a hexadecimal number is 1.
• To convert a decimal number to hexadecimal, divide the number by 16 and use the remainder to denote digits from least significant to most significant.
• Each decimal digit in Binary-Coded Decimal (BCD) representation is encoded with 4 bits.

BCD Code

• The 8-4-2-1 code is another term for BCD, representing decimal values with binary digits.

Octal and Binary Relations

• The binary equivalent of the octal number (672)8 is determined through conversion processes.
• The octal equivalent of a binary number like (101111100)2 is found by grouping bits into sets of three from the right side.

Grouping Bits for Conversion

• In binary to octal conversion, bits are grouped in sets of three.
• When forming a hexadecimal number from a binary number, bits are grouped in sets of four.

Applications in Computing

• The hexadecimal system is widely used in digital systems and computers due to its compact representation of binary data.