# 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