Number Systems

Introduction to Digital Logic - CPE2210 - 22 January 2018

Important bases

  • Decimal (base 10)
    • [0,1,2,3,4,5,6,7,8,9]
  • Binary (base 2)
    • [0,1]
  • Octal (base 8)
    • [0,1,2,3,4,5,6,7]
  • Hexadecimal (base 16)
    • [0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f]

Binary and hexadecimal is extremely important, tests and finals will test this

x92 is:

  • 1001|0010 in binary

xAC is:

  • 1100|1010 in binary

101101 is:

  • also known as 0010|1101
  • xD2 in hex

1110111 is:

  • also known as 0111|0111
  • x77 in hex

xA2 is:

  • 1010|0010 in binary
  • 2+32+128 = 162 in decimal

xD5 is:

  • 1101|0101 in binary
  • 1+4+16+64+128 = 213 in decimal

74 is:

  • 0100|1010 in binary
  • x4A in hex

82 is:

  • 0101|0010 in binary
  • x52 in hex

LSB: Least Significant Bit

  • right-most bit

MSB: Most Significant Bit

  • higher-order bit
  • left-most bit

bit: binary digit (b)

Byte: 8-bits (B)

nibble: 4-bits

high nibble left most 4 bits

low nibble right most 4 bits