Computer Organization ; Data Representation recap

Week 2: Data Representation

Deciaml, Binary, Octal, Hexadecimal

 

Convert Decimal to Binary

60(base 10)

60 - 32(2^5) = 28 - 16(2^4) = 12 - 8(2^3) = 4 - 4(2^2) = 0

111100(base 2)

 

Decimal to Octal

Division - Remainder Method

100

Binary to Octal

Separate into 3-bit chunks starting from the right

Determine the value of each 3-bit sequence

100101001000101101100(base 2)

 

100 101 001 000 101 101 100

4      5      1     0      5      5     4

 

4510554(base 8)

 

Octal to Binary

Write the 3-bit sequence for each digit

 

Binary to Hex(and vice versa)

Same as binary to octal except separate into 4-bit chunks

100101001000101101100

 

0001 0010 1001 0001 0110 1100

1         2          9       1        6       C

 

12916C(16 base)

 

Hex to Binary

12916C(16 base)

 

1         2          9       1        6       C

0001 0010 1001 0001 0110 1100

 

100101001000101101100(base 2)

 

 

Convert Fractions

 

 

Two's complement

Booth's Algorithm

https://www.grahn.us/projects/booths-algorithm/

 

Dan Grahn | Booth's Algorithm Multiplier

https://www.youtube.com/watch?v=1ubyXuXxIWU 

 

normalization rule

 

bias rule using bits of exponent