EECE 251: Digital Logic Design
Lecture: 2
Fall 2021
Tareq Hasan Khan, Ph.D.
1.2
What Does “Digital” Mean?
• Analog signal
• Digital signal
– Infinite possible values
– Finite possible values
• Ex: button pressed on a
• Ex: voltage on a wire created by microphone keypad
1
2
3
4
2
digital
signal
a
Possible values:
1.00, 1.01, 2.0000009,
... infinite possibilities
a
time
value
value
analog
signal
4
3
2
1
0
Possible values:
0, 1, 2, 3, or 4.
That’s it.
time
2
• Binary digital signal -only two possible values
– Typically represented as 0
and 1
– One binary digit is a bit
– We’ll only consider binary
digital signals
value
Digital Signals with Only Two Values:
Binary
1
0
time
3
4
5
Learning objectives
• Learning to count in Hexadecimal (Hex)
• Converting numbers
– Decimal to Binary
– Binary to Decimal
– Binary to Hex
– Hex to Binary
– Hex to Decimal
– Decimal to Hex
6
7
8
9
Learning objectives
• Learning to count in Hexadecimal (Hex)
• Converting numbers
– Decimal to Binary
– Binary to Decimal
– Binary to Hex
– Hex to Binary
– Hex to Decimal
– Decimal to Hex
10
Digits and bases of number systems
• Hexadecimal numbers use base 16
– 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
• Decimal numbers use base 10
– 0,1,2,3,4,5,6,7,8,9
• Binary numbers use base 2
– 0,1
11
Decimal (Dec) to Binary (Bin)
• Divide-By-2 Method
Repeatedly divide decimal number by 2, place remainder in current binary digit (starting from
1s column)
12
1. Divide decimal number by 2
Insert remainder into the binary number
Continue since quotient (6) is greater than 0
Decimal
6
2 12
–12
0
Binary
0
1
(current value: 0)
2. Divide quotient by 2
Insert remainder into the binary number
Continue since quotient (3) is greater than 0
3
2 6
–6
0
0 0
2 1
(current value: 0)
3. Divide quotient by 2
Insert remainder into the binary number
Continue since quotient (1) is greater than 0
1
2 3
–2
1
1 0 0
4 2 1
(current value: 4)
4. Divide quotient by 2
Insert remainder into the binary number
Quotient is 0, done
0
2 1
–0
1
1 1 0 0
8 4 2 1
(current value: 12)
Note:
Works for
any base
N—just
divide by
N instead
Binary (Bin) to Decimal (Dec)
• A byte contains 8 bits.
– b0 is the least significant bit (LSB)
– b7 is the most significant bit (MSB)
• Unsigned number can only represent positive
number.
• If a byte is used to represent an unsigned
number, then the value of the number (in
decimal) is
N = 27*b7 + 26*b6 + 25*b5 + 24*b4 +
23*b3 + 22*b2 + 21*b1 + 20*b0
13
In class exercise
• Convert 011010102 to unsigned decimal
14
Learning objectives
• Learning to count in Hexadecimal (Hex)
• Converting numbers
– Decimal to Binary
– Binary to Decimal
– Binary to Hex
– Hex to Binary
– Hex to Decimal
– Decimal to Hex
15
Binary (Bin) to Hexadecimal (Hex)
• Separate the binary numbers into groups of 4
digits (called a ‘nibble’) starting from the right.
Put leading zero’s if needed.
• Converts each group of 4 digits to one hex
digit.
16
Hexadecimal (Hex) and binary (Bin)
numbers
17
In class exercise
• Convert the following binary numbers to
hexadecimal.
101001112
1110102
18
Hexadecimal (Hex) to Binary (Bin)
• Substitute the 4-bit binary for each hex digit.
In class exercise
Convert B5D116 to binary.
19
Learning objectives
• Learning to count in Hexadecimal (Hex)
• Converting numbers
– Decimal to Binary
– Binary to Decimal
– Binary to Hex
– Hex to Binary
– Hex to Decimal
– Decimal to Hex
20
Hex to Decimal
• Method 1
– Covert Hex to Bin, then convert Bin to Hex
• Method 2
– For a hex number hn hn-1 … h1 h0, its decimal is
21
In class exercise
• Convert 3216 to unsigned decimal
22
Decimal to Hex
The steps to convert a number, let's call it N, from decimal to hex look
something like this:
1. Divide N by 16. The remainder of that division is the first (leastsignificant/right-most) digit of your hex number. Take the quotient (the
result of the division) to the next step.
1. Note: if the remainder is 10, 11, 12, 13, 14, or 15, then that becomes the hex digit
A, B, C, D, E, or F.
2. Divide the quotient from the last step by 16 again. The remainder of
this division is the second digit of your hex value (second-from-theright). Take the quotient from this division to the next step.
3. Divide the quotient from step 2 by 16 again. The remainder of this
division is the third digit of your hex conversion. Noticing a pattern?
4. Keep dividing your quotient from the last step by 16, and storing the
remainder until the result of a division is 0. The remainder of that
division is your hex value's left-most, most-significant digit.
23
• Convert 197010 to Hex
24
Announcement
• Next class:
– Binary Addition and Subtraction (Ch. 1)
25