Floating point numbers
CHIP DESIGN AND USE
Bernhard Kainz (with thanks to A. Gopalan, N. Dulay and E.
Edwards)
b.kainz@imperial.ac.uk
mailto:b.kainz@imperial.ac.uk
Integrated Circuits
• All ICs (chips) are made up of logic gates
• ICs are square pieces of silicon onto which logic gates
have been deposited
• Generally rows of pins enable connection onto a larger
circuit
wikipedia
IC – Sizes
Name Abbreviation Number of Gates
Small Scale Integrated SSI 1-10
Medium Scale Integrated MSI 10-100
Large Scale Integrated LSI 100-100,000
Very Large Scale Integrated VLSI >100,000
Example SSI Chips
7400 – Nand Gates
7404 – hex inverter
The 7400 TTL series
Example Circuit with SSI/MSI Chips
MSI Chips – Multiplexer
• A multiple-input, single-output switch
• Also called MUX for short
• sel selects which of I0 or I1 is mapped to the output
• For example, sel = 0 selects I0 and sel = 1 selects I1
• Example is called a 2-to-1 MUX
• With n selects/control lines, we can have 2n input lines
MSI Chips – Multiplexer
• 2-to-1 Multiplexer
Source: http://www.sparkfun.com/tutorials/371
MSI Chips – Multiplexer
• Truth Table
A B X A • X’ B • X Y
0 0 0 0 0 0
0 0 1 0 0 0
0 1 0 0 0 0
0 1 1 0 1 1
1 0 0 1 0 1
1 0 1 0 0 0
1 1 0 1 0 1
1 1 1 0 1 1
MSI Chips – Multiplexer
• The 3 inputs A, B, C
select which of the
input lines (D0-D7) is
copied through to the
output F
• In general, a
multiplexer has 2n
inputs and n control
lines and one output
MSI Chips – Multiplexer
• Fits nicely into a 14-pin
package (with ground
and +5V)
MSI Chips – Demultiplexer
• A single-input, multiple-output switch
• Opposite of a MUX
• Also called DEMUX
• Usually used in conjunction with a MUX
MSI Chips – Decoder
• A multiple-input, multiple-output logic circuit
• Converts coded inputs into coded outputs
• Binary Decoder has n inputs and 2n outputs
• Necessary in applications such as data multiplexing and memory
address decoding
MSI Chips – Decoder
• Only one output is 1 – the
one selected by the n-bit
binary input number – the
rest are zero
• Useful in transmitting line
selection with fewer wires
(e.g. selecting a memory
chip)
MSI Chips – Decoder
• Truth Table
A B C D7 D6 D5 D4 D3 D2 D1 D0
0 0 0 0 0 0 0 0 0 0 1
0 0 1 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 1 0 0
0 1 1 0 0 0 0 1 0 0 0
1 0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
MSI Chips – Calculations – Comparator
• To compare two numbers
• Example: 1-bit comparison
• Which gate to use?
• Recall:
MSI Chips – Calculations – Comparator
• The comparator returns 1
if the two n-bit inputs A and
B are equal, 0 otherwise
MSI Chips – Calculations – Bit-shifter
• Faster calculations for powers of 2
• Shift left and right (multiply and divide)
• c = 0 shift left
• c = 1 shift right
The Arithmetic Logic Unit (ALU)
• Digital circuit that performs arithmetic and logical operations
• Fundamental building block of the central processing unit
(CPU) of a computer
• Even the simplest microprocessors contain one for purposes such as
maintaining timers
• Processors found inside modern CPUs and graphics processing units
(GPUs) accommodate very powerful and very complex ALUs
• Concept proposed in 1945 by Mathematician John von
Neumann
• Research into ALUs remains an important part of computer
science
ALU
• Recall: Full Adder
The Arithmetic Logic Unit (ALU)
• The ALU is able to perform
multiple functions
• Depending on the input to
the decoder (F0,F1) one of
four functions is selected –
A and B, A or B, not B,
arithmetic A+B
8-bit ALU
• Can link together 1-bit ALUs to form a multi-bit ALU
• Sometimes known as bit-slice circuits
CPU Design – VLSI
• Contains millions of gates – same structure as below
CPU Design – VLSI
Production
• Good video:
• Bad video: