Binary and other number bases

Base Ten This is what we are accustomed to. Digits go from 0 – 9 Headings are represented by powers of ten ThousandsHundredsTensOnes= ,079

Other number bases Bases two- Binary Base five- Quinary Base eight- Octal Base sixteen - Hexadecimal Bases are named for their “headings.”

Base Two Uses only 1’s and 0’s Headings are in powers of two Headings Binary number

Base Two – converting to decimal Headings Binary number = = 76 Question: Convert to a decimal (base ten) number Answer:

Base Eight Uses digits from 1 to 7 Headings are in powers of eights Headings Binary number

Base Eight – converting to decimal Headings Binary number = = 94 Question: Convert to a decimal (base ten) number Answer:

Base Sixteen Uses digits from 1 to 9, and letters from A to F (10 to 15) Headings are in powers of 16’s 161 2B Headings Binary number

Base Eight – converting to decimal 161 2B Headings Binary number = = 43 Question: Convert 2B 16 to a decimal (base ten) number Answer:

Review: Binary to Decimal WEUs WEUs New: Converting a decimal to binary 2ZQM 2ZQM

Binary addition Basic rules = and carry 1 1 and carry 1

Binary addition example =11101 Carry’s Answer

Binary addition video w_E4 w_E4

Other binary BCD – Binary Coded Decimal Every digit of a number is represented using its 4-bit binary equivalent The number is not “converted,” instead each digit is given a “code”

0=0000 1=0001 2=0010 3=0011 4=0100 5=0101 6=0110 7=0111 8=1000 9=1001 A negative sign is represented by 1011

BCD exampl Convert 473 to binary coded decimal Answer: = We can separate the answer by spaces

BCD example 2 Convert -93 to SIGNED BCD Answer: =

Try this! What number does BCD represent? Answer: = Answer: 591