Chapter 6

Question 1

In modern computer adder reside in the ______________________ but also in other parts of the processor, where they are used to calculate addresses, table indices, and similar operations.

Answer 1

arithmetic logic unit (ALU)

Question 2

The ___________ adds two single binary digits A and B. It has two outputs, sum (S) and carry (C). The carry signal represents an overflow into the next digit of a multi-digit addition.

Answer 2

half adder

Question 3

The simplest half-adder design incorporates an XOR gate for ______ and an AND gate for _______. With the addition of an OR gate to combine their carry outputs, two half adders can be combined to make a __________

Answer 3

Sum, Carry, full adder.

Question 4

A ____________ adds binary numbers and accounts for values carried in as well as carry out.

Answer 4

full adder

Question 5

A one-bit full adder adds three one-bit numbers, often written as A, B, and Cin; A and B are the __________, and Cin is a _____________ in from the next less significant stage.

Answer 5

operands, bit carried

Question 6

A one-bit full adder adds three one-bit numbers, often written as A, B, and Cin; A and B are the __________, and Cin is a _____________ in from the next less significant stage.

Answer 6

operands, bit carried

Question 7

The full-adder is usually a component in a __________ of adders, which add 8, 16, 32, etc. binary numbers.

Answer 7

cascade

Question 8

The output carry (C4) is not ready until it propagates through all of the full adders. This is called ____________, delaying the addition process. Each carry bit “ripples” to the next full adder. Note that the first (and only the first) full adder may be replaced by a half adder.

Answer 8

ripple carry

Question 9

The ripple-carry adder is relatively ______, since each full adder must wait for the carry bit to be calculated from the previous full adder.

Answer 9

slow

Question 10

ripple carry adder… To reduce the computation time, engineers devised faster ways to add two binary numbers by using ________________

Answer 10

carry-lookahead adders.

Question 11

A carry-lookahead adder improves speed by reducing the amount of _____ required to determine carry bits.

Answer 11

time

Question 12

It can be contrasted with the simpler, but usually slower, ripple carry adder for which the carry bit is calculated alongside the sum bit, and each bit must wait until the previous carry has been calculated to begin calculating its own result and carry bits.
#Footnote
Readings

Question 13

The carry-lookahead adder calculates ___________ carry bits before the sum, which reduces the wait time to calculate the result of the larger value bits.

Answer 13

one or more

Question 14

Carry-Lookahead adder
They work by creating two signals (P and G) for each bit position, based on whether a carry is propagated through from a less significant bit position (at least one input is a ‘1’), generated in that bit position (both inputs are ‘1’), or killed in that bit position (both inputs are ‘0’).
#footnote readings

Question 15

In most cases, P is simply the ______ output of a half-adder and G is the ________ output of the same adder. After P and G are generated the carries for every bit position are created. Aa

Answer 15

sum, carry

Question 16

Footnote readings

Subtraction is generally simpler than addition since only two numbers are involved and the upper value representation is greater than the lower value representation. The problem of “borrow” is similar in binary subtraction to that in decimal.

Question 17

Footnote readings

Subtraction is generally simpler than addition since only two numbers are involved and the upper value representation is greater than the lower value representation. The problem of “borrow” is similar in binary subtraction to that in decimal.