Did they have computers in The Giver?

The community does have computers and advanced technology. 

Jonas does have at least some understanding of the workings of a computer.  When Jonas and The Giver discuss memory, Jonas tells the old man that he understands what memory is because he has learned about it in school. 

"My Instructors in science and technology have taught us about how the brain works," Jonas told him eagerly. "It's full of electrical impulses. It's like a computer....

The community does have computers and advanced technology. 

Jonas does have at least some understanding of the workings of a computer.  When Jonas and The Giver discuss memory, Jonas tells the old man that he understands what memory is because he has learned about it in school. 

"My Instructors in science and technology have taught us about how the brain works," Jonas told him eagerly. "It's full of electrical impulses. It's like a computer. If you stimulate one part of the brain with an electrode, it--" (Ch. 13) 

The Giver tells him that they “know nothing.”  The community has tight control over everything, a concept called Sameness.  Part of this involves very adept use of technology and an interesting use of memories.  We are never really told exactly how the community accomplishes its technological tasks, but they clearly have advanced technology. 

Technology is an important part of everyone’s everyday life too.  Children learn about it in school, and once they turn twelve they learn the technology required for their new Assignments. 

School was less important to him now; and before much more time passed, his formal schooling would end. But still, for Twelves, though they had begun their adult training, there were the endless lists of rules to be memorized and the newest technology to be mastered. (Ch. 17) 

Again, we are not given much detail.  Science and technology are usually mentioned together.  The community has advanced technology in areas of genetic engineering, technology, and biomechanics.  We do not know what technology they have, but we know they have at least most of the technology that we have and then some.  After all, they can control memories, color, the climate, and genetics.  Sometimes these are used against the citizens.  When Jonas escapes, he remembers that he learned in science and technology classes about heat-sensing search planes, and he avoids them.