Page 93 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes important concepts in the theory of combinatorial games is that of the sum of two games,
which is a game where each player may choose to move either in one game or the other at any
point in the game, and a player wins when his opponent has no move in either game. This
way of combining games leads to a rich and powerful mathematical structure.
John Conway states in ONAG that the inspiration for the theory of partisan games was based
on his observation of the play in go endgames, which can often be decomposed into sums of
simpler endgames isolated from each other in different parts of the board.
Questions:
1. Explain the concept of combinational game theory.
2. Who was the founder of game theory?

Self Assessment

Choose the correct answer:
6. Priority encoder: Each input has a priority level associated with it. The encoder outputs
indicate the active input that has the highest priority.
(a) True (b) False
7. Decoder is a logic circuit with n inputs and .......... outputs.
(a) n 2 (b) 2 n
(c) 1 (d) n + 1
2
8. Which digital system translates coded characters into a more useful form?
(a) Encoder (b) Display
(c) Counter (d) Decoder

9. How many inputs are required for a 1-of-10 BCD decoder?
(a) 4 (b) 8
(c) 10 (d) 1

5.5 Summary

• The full adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. binary
numbers.
• Decoders are useful for many practical purposes. We showed the sum-of products
implementation of the 4-to-1 multiplexer, which requires AND gates to distinguish the
four different valuations of the select inputs s1 and s0.
• A full subtractor has the borrow-in capability and so allows cascading which results in the
possibility of multi-bit subtraction.
• The purpose of the decoder and encoder circuits is to convert from one type of input
encoding to a different output encoding.
• The half-subtractor is a combinational circuit which is used to perform subtraction of two
bits.

5.6 Keywords

Adder: This is a digital circuit that performs addition of binary numbers. In modern computers
adders reside in the arithmetic logic unit (ALU).

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