Digital Design
CPEN 214 - Digital Logic Design Binary Systems
C. Gerousis © Digital Design 3rd Ed., Mano Prentice Hall
Digital vs. Analog
• An analog system has continuous range of values
– A mercury thermometer – Vinyl records – Human eye
• A digital system has a set of discrete values
– Digital Thermometer – Compact Disc (CD) – Digital camera
Benefits of using digital
Analog signal
Digital signal
• Advantages of using Digital: • Cheap electronic circuits • Easier to calibrate and adjust • Resistance to noise: Clearer picture and sound
Binary System
• Discrete elements of information are represented with bits called binary codes. Example: (09)10 = (1001)2 (15)10 = (1111)2 Question: Why are commercial products made with digital circuits as opposed to analog? Most digital devices are programmable: By changing the program in the device, the same underlying hardware can be used for many different applications.
Decimal Code
4 Review the decimal number system.
Base (Radix) is 10 - symbols (0,1, . . 9) Digits For Numbers > 9, add more significant digits in position to the left, e.g. 19>9. Each position carries a weight. MSD Weights: ü
103 102 101 100 10−110−2 10−3
LSD
If we were to write 1936.25 using a power series expansion and base 10 arithmetic:
1× 103 + 9 × 102 + 3× 101 + 6 × 100 + 2 × 10−1 + 5 × 10−2
Binary number system
4 The binary number system.
– – – Base is 2 - symbols (0,1) - Binary Digits (Bits) For Numbers > 1, add more significant digits in position to the left, e.g. 10>1. Each position carries a weight (using decimal).
MSD Weights:
23 2 2 21 2 0
2 −1 2 −2 2 −3
LSD
ü If we write 10111.01 using a decimal power series we convert from binary to decimal:
1× 24 + 0 × 23 + 1× 22 + 1× 21 + 1× 20 + 0 × 2−1 + 1× 2 −2 = = 1× 16 + 0 × 8 + 1× 4 + 1× 2 + 1× 1 + 0 × 0.5 + 1× 0. 25 = 23.25
Binary number system q (110000.0111)2 = ( ? )10
ANS: 48.4375
4 In computer work: 210 =1024 is referred as K = kilo
220 =1048576 is referred as M = mega 230 = ? 240 = ? q
C. Gerousis © Digital Design 3rd Ed., Mano Prentice Hall
Digital vs. Analog
• An analog system has continuous range of values
– A mercury thermometer – Vinyl records – Human eye
• A digital system has a set of discrete values
– Digital Thermometer – Compact Disc (CD) – Digital camera
Benefits of using digital
Analog signal
Digital signal
• Advantages of using Digital: • Cheap electronic circuits • Easier to calibrate and adjust • Resistance to noise: Clearer picture and sound
Binary System
• Discrete elements of information are represented with bits called binary codes. Example: (09)10 = (1001)2 (15)10 = (1111)2 Question: Why are commercial products made with digital circuits as opposed to analog? Most digital devices are programmable: By changing the program in the device, the same underlying hardware can be used for many different applications.
Decimal Code
4 Review the decimal number system.
Base (Radix) is 10 - symbols (0,1, . . 9) Digits For Numbers > 9, add more significant digits in position to the left, e.g. 19>9. Each position carries a weight. MSD Weights: ü
103 102 101 100 10−110−2 10−3
LSD
If we were to write 1936.25 using a power series expansion and base 10 arithmetic:
1× 103 + 9 × 102 + 3× 101 + 6 × 100 + 2 × 10−1 + 5 × 10−2
Binary number system
4 The binary number system.
– – – Base is 2 - symbols (0,1) - Binary Digits (Bits) For Numbers > 1, add more significant digits in position to the left, e.g. 10>1. Each position carries a weight (using decimal).
MSD Weights:
23 2 2 21 2 0
2 −1 2 −2 2 −3
LSD
ü If we write 10111.01 using a decimal power series we convert from binary to decimal:
1× 24 + 0 × 23 + 1× 22 + 1× 21 + 1× 20 + 0 × 2−1 + 1× 2 −2 = = 1× 16 + 0 × 8 + 1× 4 + 1× 2 + 1× 1 + 0 × 0.5 + 1× 0. 25 = 23.25
Binary number system q (110000.0111)2 = ( ? )10
ANS: 48.4375
4 In computer work: 210 =1024 is referred as K = kilo
220 =1048576 is referred as M = mega 230 = ? 240 = ? q