This document provides an overview of digital computer fundamentals, including combinational logic circuits, binary adders, half adders and full adders, binary subtraction, multiplexers, decoders, encoders, and floating point number systems. Combinational logic is used to perform calculations in circuits like arithmetic logic units. Binary adders perform addition of binary numbers using full-adder circuits connected in series. Half adders and full adders are basic adder circuits classified by the number of inputs. Decoders and encoders are circuits that convert between binary codes and encoded representations. Floating point numbers represent values with a radix point that can vary, allowing a wide range of numbers to be stored.

1. DIGITAL COMPUTER FUNDAMENTALS
Presented by
G.Vinothini M.sc.,M.phil.,
Department of Information Techonology,
Bon Secours College for Women,
Thanjavur.

2. COMBINATIONAl LOGIC CIRCUITS
Combinational logic is used in computer circuits to
perform Boolean algebra on input signals and on stored data.
Practical computer circuits normally contain a mixture of
combinational and sequential logic. For example, the part of
an arithmetic logic unit, or ALU, that does mathematical
calculations is constructed using combinational logic. Other
circuits used in computers, such as half adders, full adders, half
subtractors, full
subtractors, multiplexers, demultiplexers, encoders and decoder
s are also made by using combinational logic.

3. • The Add micro-operation requires registers that can hold the data and the
digital components that can perform the arithmetic addition.
• A Binary Adder is a digital circuit that performs the arithmetic sum of two
binary numbers provided with any length.
• A Binary Adder is constructed using full-adder circuits connected in
series, with the output carry from one full-adder connected to the input
carry of the next full-adder.
BINARY ADDERS:

4. HALF ADDERS AND FULL ADDERS:
• An adder is a digital logic circuit in electronics that
implements addition of numbers.
• Adders are classified into two types: half adder and
full adder. The half adder circuit has two inputs: A
and B, which add two input digits and generate a
carry and sum. The full adder circuit has three
inputs: A and C, which add the three input
numbers and generate a carry and sum.

5. BCD ADDERS:
BCD adder A 4-bit binary adder that is
capable of adding two 4-bit words having
a BCD (binary-coded decimal) format. The
result of the addition is a BCD-format 4-bit
output word, representing the decimal sum of
the addend and augend, and a carry that is
generated if this sum exceeds a decimal value
of 9.

6. BINARY SUBTRACTIONS:
Binary Subtraction. Binary subtraction is also
similar to that of decimal subtraction with the
difference that when 1 is subtracted from 0, it
is necessary to borrow 1 from the next higher
order bit and that bit is reduced by 1

7. HALF AND FULL
SUBTRACTIONS:Subtractor circuits take two binary numbers
as input and subtract one binary number
input from the other binary number input.

8. MULTIPLEXER (4:1) :
4x1 Multiplexer has four data inputs
I3, I2, I1 & I0, two selection lines s1 &
s0 and one output Y. The block
diagram of 4x1 Multiplexer.

9. 1 TO 4 LINES DEMULTIPLEXER:
The input data goes to any one of the
fouroutputs at a given time for a
particular combination of select lines.
Thisdemultiplexer is also called as a 2-
to-4 demultiplexer which means that two
selectlines and 4 output lines.

10. A decoder is a circuit that changes a code
into a set of signals. It is called
a decoderbecause it does the reverse of
encoding, but we will begin our study of
encoders
anddecoders with decoders because they
are simpler to design.
DECODERS:

11. DECODERS : BCD TO DECIMAL
BCD-to-Decimal decoders include the
TTL 7442 or the CMOS 4028. Generally
a decoders output code normally has
more bits than its input code and
practical “binary decoder” circuits
include, 2-to-4, 3-to-8 and 4-to-16 line
configurations.

12. BCD TO SEVEN SEGMENTS:
A BCD to Seven Segment decoder is a
combinational logic circuit that accepts a
decimal digit in BCD (input) and generates
appropriate outputs for
the segments todisplay the input decimal
digit.

13. ENCODERS:
A simple encoder or simply an encoder in digital electronics is
a one-hot to binary converter. That is, if there are 2ⁿ input lines,
and at most only one of them will ever be high, the binary code
of this 'hot' line is produced on the n-bit output lines.

14. ENCODERS: 4:2 LINES
digital encoders produce outputs of 2-bit, 3-
bit or 4-bit codes depending upon the
number of data input lines. An “n-bit”
binary encoder has 2n input lines and n-bit
output lines with common types that
include4-to-2, 8-to-3 and 16-to-4 line

15. ENCODERS: OCTAL TO BINARY
The octal-to-binary encoder consists of eight
inputs, one for each of the eight digits, and three
outputs that generate the
corresponding binary number. It is constructed with
OR gates whose inputs can be determined from the
truth table given in Table 2. The low-order output bit z
is 1 if the input octal digit is odd.

16. FLOATING POINT NUMBER
SYSTEM:
The term floating point refers to the fact that
a number's radix point (decimal point, or, more commonly
in computers, binary point) can "float"; that is, it can be
placed anywhere relative to the significant digits of
thenumber.

18. RANGE OF STORED NUMBERS:
Number of bits Formula Range
8 2
8
- 1 0 - 255
16 2
16
- 1 0 - 65,535
24 2
24
- 1 0 - 16,777,215
32 2
32
- 1 0 - 4, 294,967,295