Here is the assignment with an outline. Let me know if you have any other questions! 😀

Digital Building Blocks
1.Chapter Concepts Outline
o 5.1 Introduction:
• Building blocks: Each has a well-defined interface and can be treated as a black box
when the underlying implementation is unimportant, easily extended to different sizes.
o 5.2 Arithmetic Circuits:
• Arithmetic circuits: central building blocks of computers
• Addition: one of the most common operations in digital systems
• Half adder: has two inputs, A and B, and two outputs, S and C out. It can be built from an
XOR gate and an AND gate.
• Multi-bit adder: C out is added or carried in to the next most significant bit.
• Full adder: accepts the carry in, C in.
• Carry propagate adder: also known as an N-bit adder, it sums two N-bit inputs, A and B,
and a carry in, C in, to produce an N-bit result, S, and a carry out, C out.
• Ripple-carry adder: The C out of one stage acts as the C in of the next stage, it is a good
application of modularity and regularity, has the disadvantage of being slow when N is
large.
• Carry-lookahead adder: another type of carry propagate adder that solves the problem of
slowness by dividing the adder into blocks and providing circuitry to quickly determine
the carry out of a block as soon as the carry in is known.
• Generate: The ith column of an adder is said to generate a carry if it produces a carry out
independent of the carry in.
• Propagate: The column is said to propagate a carry if it produces a carry out whenever
there is a carry in.
• Prefix adder: extends the generate and propagate logic of the carry-lookahead adder to
perform addition even faster.
• Prefixes: block generate signals.
• Subtraction: while adders can add positive and negative numbers using two’s
complement number representation, subtraction is almost as easy: flip the sign of the
second number, then add.
• Comparator: determines whether two binary numbers are equal or if one is greater or less
than the other.
• Equality comparator: produces a single output indicating whether A is equal to B (A = =
B).
• Magnitude comparator: produces one or more outputs indicating the relative values of A
and B.
• Arithmetic/Logical Unit (ALU): combines a variety of mathematical and logical
operations into a single unit.
• Zero extend unit: produces an N-bit output by concatenating its 1-bit input with 0’s in the
most significant bits.
• Flags: when ALS’s produce extra outputs.

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Overflow flag: indicates that the result of the adder overflowed.
Zero flag: indicates that the ALU output is 0.
Shifters: move bits and multiply or divide by powers of 2.
Logical shifters: shifts the number to the left (LSL) or right (LSR) and fills empty spots
with 0’s.
• Arithmetic shifter: is the same as a logical shifter, but on right shifts fills the most
significant bits with a copy of the old most significant bit (msb).
• Rotator: rotates number in circle such that empty spots are filled with bits shifted off the
other end.
• Left shift: a special case of multiplication, multiplies the number by 2 to the n.
• An arithmetic right shift: a special case of division, divides the number by 2N.
• Multiplication unsigned binary numbers: similar to decimal multiplication but involves
only 1’s and 0’s.
• Partial products: formed by multiplying a single digit of the multiplier with the entire
multiplicand.
• Partial remainder (R): initialized to the dividend, A.
o 5.3 Number Systems:
• Fixed-point numbers: analogous to decimals; some of...